Sparse direction-of-arrival (DOA) estimation of wideband signal has attracted widespread researches for its unique high-resolution performance. Numerous existing methods based on sparse Bayesian learning (SBL) don’t possess the ability to enhance sparsity even if they have already enjoyed high favor among sparse recovery approaches. In view of this, we propose a novel hierarchical Bayesian prior framework that enhance sparsity evidently and derive its corresponding iterative algorithm. On analysis, the computational complexity of the iterative are less than most existing other state-of-the-art algorithms. Not only that, proposed method possesses high angular estimation precision and sparsity performance by utilizing joint sparsity of multiple measure vector (MMV) models. Last but not least, the method obtains the ability to stabilize the estimated values between different frequencies or snapshots such that flat spatial spectrum. Extensive simulation results are presented to prove the superior performance of our methods

Estimating parameters for multiple datasets can be time consuming, especially when the number of datasets is large. One solution is to sample from multiple datasets simultaneously using Bayesian methods such as adaptive multiple importance sampling (AMIS). Here we use the AMIS approach to fit a von Misses distribution to multiple datasets for wind trajectories derived from a Lagrangian Particle Dispersion Model driven from a 3D meteorological data. The primary objective is to characterise the uncertainties in wind trajectories in a form that can be used as inputs for predictive models of wind-dispersed insect pests and pathogens of agricultural crops for use in evaluating risk and in planning mitigation actions. Our results show that AMIS can significantly improve the efficiency of parameter inference for multiple datasets.

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

By combining stochastic variational inference with message passing algorithms we show how to solve the highly complex problem of navigation and avoidance in distributed multi-robot systems in a computationally tractable manner, allowing online implementation. Subsequently, the proposed variational method lends itself to more flexible solutions than prior methodologies. Furthermore, the derived method is verified both through simulations with multiple mobile robots and a real world experiment with two mobile robots. In both cases the robots shares the operating space and needs to cross each other’s paths multiple times without colliding.

In this paper, we focus on variational Bayesian learning deterministic optimization methods for inference in biparametric exponential models where the parameters follow semiparametric regression structures. This combination of data models and algorithms contributes to solving real-world problems and reduces the computation time. This allows both the rapid exploration of many data models and the accurate estimation of the mean and variance functions through the connection between generalized linear models and graph theory. A simulation study was carried out to assess the performance of the deterministic approximation. Finally, herein, we present an application using macroeconomic data to emphasize the benefits of the proposed approach.

In many Bayesian computations, first, we obtain the expression of the joint distribution of all the unknown variables given the observed data. In general, this expression is not separable in those variables. Thus, obtaining their marginals for each variable and computing the expectations are difficult and costly. This problem becomes even more difficult in high dimensional quandaries, which is an important issue in inverse problems. We may then try to propose a surrogate expression with which we can do approximate computations. Often a separable expression approximation can be useful enough. The Variational Bayesian Approximation (VBA) is a technique that approximates the joint distribution $p$ with an easier, for example separable, one $q$ by minimizing Kullback–Leibler Divergence $KL(q|p)$. When $q$ is separable in all the variables, the approximation is also called Mean Field Approximation (MFA) and so $q$ is the product of the approximated marginals. A first standard and general algorithm is alternate optimization of $KL(q|p)$ with respect to $q_i$. A second general approach is its optimization in the Riemannian manifold. However, in this paper, for practical reasons, we consider the case where $p$ is in the exponential family and so is $q$. For this case, $KL(q|p)$ becomes a function of the parameters $\thetab$ of the exponential family. Then, we can use any other optimization algorithm to obtain those parameters. In this paper, we compare three optimization algorithms: standard alternate optimization, a gradient-based algorithm and a natural gradient algorithm and study their relative performances on three examples.

The description of stellar interiors remains as a big challenge for the nuclear astrophysics community. The consolidated knowledge is restricted to density regions around the saturation of hadronic matter $\rho _{0} = 2.8\times 10^{14} {\rm\ g\ cm^{-3}}$, regimes where our nuclear models are successfully applied. As one moves towards higher densities and extreme conditions up to five to twenty times $\rho_{0}$, little can be said about the microphysics of such obejects. Here, we employ an MCMC strategy in order to access the variability of polytropic three-pircewised models for neutron star equation of states. With a fixed description of the hadronic matter we explore a variety of models for the high density regimes leading to stellar masses up to 2.5 $M_{\odot}$. In addition, we also discuss the use of a Bayesian power regression model with heteroscedastic error. The set of EoS from LIGO was used as inputs and treated as data set for testing case.

This paper investigates an inverse problem of option pricing in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of MCMC enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown drift and volatility coefficients from the measured data.

In this study, based on our previous study, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient booms and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute vibrations of actual data by means of our proposed model.

Quantile regression model is widely used in variable relationship research of general size data, due to strong robustness and more comprehensive description of the response variables' characteristics. With the increase of data size and data dimension, there have been some studies on high-dimensional quantile regression under the classical statistical framework, including higher-efficient frequency perspective, which is however at cost of randomness quantification, or lower-efficient Bayesian method based on MCMC sampling. To overcome these problems, we propose the high-dimensional quantile regression with Spike-and-Slab Lasso penalty based on variational Bayesian (VBSSLQR), which can not only improve the computational efficiency but also measure the randomness via variational distributions. The simulation studies and real data analysis illustrate that the proposed VBSSLQR method is superior to or equivalent to other quantile and non-quantile regression methods (including Bayesian and non-Bayesian methods), and its efficiency is higher than any other method.

Bayesian techniques for engineering problems, that rely on Gaussian process (GP) regression, are known for their ability to quantify epistemic and aleatory uncertainties and for being data efficient. The mathematical elegance of applying these methods usually comes at a high computational cost when compared to deterministic and empirical Bayesian methods. Furthermore, using these methods becomes practically infeasible in scenarios characterized by a large number of inputs and thousands of training data. The focus of this work is on enhancing Gaussian Process-based metamodeling and model calibration tasks, when the size of the training datasets is significantly large. To achieve this goal, we employ a stochastic variational inference algorithm that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference. The numerical performance of the algorithm is demonstrated on multiple metamodeling and model calibration problems with thousands of training data.

The giant challenge breeding flood-irrigated rice is to identify superior genotypes that present high-yielding with specific grain qualities, resistance to abiotic and biotic stresses, excellent adaptation to the target environment. Thus, the objectives of this study were to propose a bayesian multi-trait model, estimate genetic parameters, and select flood-irrigated rice genotypes with better genetic potentials in different evaluation environments. For this, twenty-five rice genotypes belonging to the flood-irrigated rice improvement program were evaluated. The grain yields, grain length, width and thickness, grain length, and grain width and weight of 100 grains in the agricultural year 2016/2017. The experimental design used in all experiments was a randomized block design with three replications. The Monte Carlo Markov Chain algorithm estimated genetic parameters and genetic values. The grain thickness trait was considered highly heritable, with a credibility interval ranging from: h^2: 0.9480; 0.9440; 0.8610, in environments 1, 2, and 3, respectively. The grain yields showed a low correlation estimate between grain thickness and 100-grain weight, in all environments, with a credibility interval ranging from (ρ= 0.5477; 0.5762; 0.5618 and 0.5973; 0.5247; 0.5632, grain thickness and 100-grain weight, in environments 1, 2, and 3, respectively). The Bayesian multi-trait model proved to be an adequate strategy for the genetic improvement of flood-irrigated. Genotypes 2 and 15 had similar potential in the three environments, they should be selected as high-performance multi-trait genotypes for the genetic breeding of flood-irrigated rice in the program.

Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of the solution, without calculating the full inversion operator and the complete solution. It is a well-known fact about partial differential equations that the solution at each discretisation point depends on the solutions at all other discretisation points. Therefore, it is impossible to compute the solution only at one point, without calculating the solution at all other points. The standard numerical methods like a conjugate gradient or Gauss elimination compute the whole solution and/or the complete inverse operator. We suggest a method which can compute the solution of the given partial differential equation 1) at a point; 2) at few points; 3) on an interface; or a functional of the solution, without computing the solution at all points. The required storage cost and computational resources will be lower as in the standard approach. With this new method, we can speed up, for instance, computation of the innovation in filtering or the likelihood distribution, which measures the data misfit (mismatch). Further, we can speed up the solution of the regression, Bayesian inversion, data assimilation, and Kalman filter update problems. Applying additionally the hierarchical matrix approximation, we reduce the cubic computational cost to almost linear $\mathcal{O}(k^2n \log^2 n)$, where $k\ll n$ and $n$ is the number of degrees of freedom. Up to the hierarchical matrix approximation error, the computed solution is exact. One of the disadvantages of this method is the need to modify the existing deterministic solver.

This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

Background: Coronavirus disease 2019 (COVID-19) pandemic are causing significant damages to many nations. For mitigating its risk, Japan’s Prime Minister called on all elementary, junior high and high schools nationwide to close beginning March 1, 2020. However, its effectiveness in decreasing disease burden has not been investigated. Methods: We used daily data on the report of COVID-19 and coronavirus infection incidence in Japan until March 31, 2020. Time series analysis were conducted using Bayesian method. Local linear trend models with interventional effect were constructed for number of newly reported cases of COVID-19, including asymptomatic infections. We considered that the effects of intervention start to appear 9 days after the school closure; i.e., on March 9. Results: The intervention of school closure did not appear to decrease the incidence of coronavirus infection. If the effectiveness of school closure began on March 9, mean coefficient α for effectiveness of the measure was calculated to be 0.08 (95% credible interval -0.36 to 0.65), and the actual reported cases were more than predicted, yet with rather wide credible interval. Sensitivity analyses using different dates also showed similar results. Conclusions: School closure carried out in Japan did not show the effectiveness to mitigate the transmission of novel coronavirus infection.

In his best-selling book An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg Paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair coin. A natural generalization of his method is to establish the entrance fee for the case in which the probability of head is θ (0 < θ < 1/2). The deduction of those fees is the main result of Section 2. We then propose a Bayesian approach to the problem. When the probability of head is θ (1/2 < θ < 1) the expected gain of the St. Petersburg Game is finite, therefore there is no paradox. However, if one takes θ as a random variable assuming values in (1/2,1) the paradox may hold, what is counter-intuitive. On Section 3 we determine a necessary and sufficient condition for the absence of paradox on the Bayesian approach and on Section 4 we establish the entrance fee for the case in which θ is uniformly distributed in (1/2,1), for in this case there is paradox.

Aiming at the problem that the performance of Adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement noise matrix are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of Multi-fading factor and update monitoring strategy adaptive Kalman filter based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model, the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the update monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices.

Semi-continuous data are very common in the social science and economics. In this paper, a Bayesian variable selection procedure is developed to assess the influence of exogenous factors including observed and unobserved on the semi-continuous data. Our formulation is based on the two-part latent variable model with polytomous response. We consider two schemes for the penalties of regression coefficients and factor loadings: the Bayesian spike and slab bimodal prior and the Bayesian lasso prior. Within the Bayesian framework, we implement Markov Chains Monte Carlo sampling method to conduct posterior inference. To facilitate posterior sampling, we recast the logistic model in part one as the norm-like mixture model. Gibbs sampler is designed to draw observations from the posterior. Our empirical results show that with suitable hyper-parameters, the spike and slab bimodal method slightly outperforms the Bayesian lasso in the current analysis. Finally, a real example related to the China household finance survey is analyzed to illustrate the application of the methodology.. .

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences, notably lifetime, medical, and financial sciences. The Heavy tailed Nadarajah Haghighi model is introduced by compounding the heavy tailed family and Nadarajah Haghighi distribution in this paper. The so obtained model has three parameters accounting for the scale and shape of the distribution. The proposed distribution's fundamental characteristics such as probability density, cumulative distribution, hazard rate, and survival functions are provided, and several key statistical properties are established, and several entropy information measures are proposed. The estimation of model parameter is performed via the ML procedure. Further, different simulation experiments are conducted to demonstrate the performance of proposed estimator’s using some measure, like the average estimate, the average bias, and associated mean square error. Finally, we are applied our proposed model to analyze three different real datasets. In our illustration, we are compared the practicality of the recommended model with several well-known competing models.

In this paper, we consider a class of bilevel programming problems (abbreviated as, BLPP). Exploiting the generalized approximate convexity assumptions, we investigate the relations among the solutions of approximate Minty (respectively, Stampacchia) type variational inequalities (abbreviated as, AMTVI (respectively, ASTVI)), and the local ϵ-quasi solutions of the BLPP. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (abbreviated as, KKM)-Fan’s lemma, we derive some existence results for the solutions of approximate variational inequalities (abbreviated as, AVI), namely, AMTVI and ASTVI. A non-trivial example is given to highlight the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that establishes relationships between the AVI and the BLPP under the assumptions of generalized approximate convexity in terms of limiting subdifferentials.

ACL instability poses a significant challenge in traumatology and orthopedic medicine, often requiring accurate diagnosis for appropriate treatment. While the pivot-shift test offers a crucial means of assessment, its reliance on subjective interpretation underscores the need for supplementary imaging studies. This study aims to address this limitation by developing a Bayesian classification algorithm tailored for integration into a mobile application. Using the built-in inertial sensors of smartphones, this new approach aims to dynamically evaluate rotational stability during knee examinations. Orthopedic specialists conducted knee evaluations on 52 subjects, with subsequent analysis revealing interesting insights. Intraobserver and interobserver analyses, as measured by ICC, demonstrated strong agreement both in terms of timing between maneuvers (ICC = 0.94) and signal amplitude (ICC = 0.71-0.66). Notably, the Bayesian algorithm successfully classified 95% of joint hypermobility cases, with an additional 7 cases of hyperlaxity identified by the Pivot-Shift Meter (PSM). These findings highlight the practicality and effectiveness of implementing a Bayesian classification algorithm within a mobile application for assessing and categorizing signals captured by smartphone inertial sensors during the pivot-shift test.

It is increasingly common for experiments in biology and medicine to involve large numbers of hypothesis tests. A natural graphical method for visualizing these tests is to construct a histogram from the p-values of these tests. In this article, we examine the shapes, both normal and abnormal, that these histograms can take on, as well as present simple inferential procedures that help to interpret the shapes in terms of diagnosing potential problems with the experiment. We examine potential causes of these problems in detail, and discuss potential remedies. Throughout, examples of abnormal-looking p-value histograms are provided and based on case studies involving real biological experiments.

In this paper we explore the known connection among sustainability, resilience, and well-being within the framework of active inference. Initially, we revisit how the notions of well-being and resilience intersect within active inference before defining sustainability. We adopt a holistic concept of sustainability denoting the enduring capacity to meet needs over time without depleting crucial resources. It extends beyond material wealth to encompass community networks, labor, and knowledge. Using the Free Energy Principle, we can emphasize the role of fostering resource renewal, harmonious system-entity exchanges, and practices that encourage self-organization and resilience as pathways to achieving sustainability, both in an agent and in collectives. We start by connecting Active Inference with well-being, building on exsiting work. We then attempt to link resilience with sustainability, asserting that resilience alone is insufficient for sustainable outcomes. While crucial for absorbing shocks and stresses, resilience must be intrinsically linked with sustainability to ensure that adaptive capacities do not merely perpetuate existing vulnerabilities. Rather, it should facilitate transformative processes that address the root causes of unsustainability. Sustainability, therefore, must manifest across extended timescales and all system strata, from individual components to the broader system, to uphold ecological integrity, economic stability, and social well-being. We explain how sustainability manifests at the level of an agent, and then at the level of collectives and systems. To model and quantify the interdependencies between resources and their impact on overall system sustainability, we introduce the application of network theory and dynamical systems theory. We emphasize the optimization of precision or learning rates through the active inference framework, advocating for an approach that fosters the elastic and plastic resilience necessary for long-term sustainability and abundance.

Fitting parameters on spline curves produces more parsimonious models, maintaining fit quality. Smoothing the splines reduces predictive variance. Individual splines are often fit by type of variable, e.g., in age-period-cohort models. Linear and cubic splines are most common. Several smoothing criteria have been used for parameter curves, with cubic splines fit by constraining the integral of splines’ squared-second derivatives popular recently. Constraining the sum of squared second differences for linear splines is analogous. Generally the degree of smoothing is selected using cross-validation. Known spline dummy-variable matrices allow regression estimation of splines, with smoothing done via constrained regression. Smoothing criteria based on sums of squares or absolute values of parameters, as in ridge regression or LASSO, improves predictive accuracy and produces splines similar to smoothing by second-derivative constraints. Variables with very low t-statistics represent points where curve-shapes barely change. Eliminating those variables leaves knots concentrated where spline shapes change. A Bayesian version of this puts shrinkage priors on spline parameters. This yields realistic joint parameter distributions, avoids problems associated with using cross-validation for parameter estimation, and readily expands to non-linear modeling, such as interactions among variable types. Regularized regression and Bayesian spline methods are compared for two example datasets.

Energy Measurement and Verification (M&V) aims to make inferences about the savings achieved in energy projects, given the data and other information at hand. Traditionally, a frequentist approach has been used to quantify these savings and their associated uncertainties. We demonstrate that the Bayesian paradigm is an intuitive, coherent, and powerful alternative framework within which M&V can be done. Its advantages and limitations are discussed, and two examples from the industry-standard International Performance Measurement and Verification Protocol (IPMVP) are solved using the framework. Bayesian analysis is shown to describe the problem more thoroughly and yield richer information and uncertainty quantification than the standard methods while not sacrificing model simplicity. We also show that Bayesian methods can be more robust to outliers. Bayesian alternatives to standard M&V methods are listed, and examples from literature are cited.

Variational Auto-Encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the Simplicial Auto-Encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a data set better than a standard VAE.

The free energy principle (FEP) is a mathematical and scientific principle that describes the relationship between the physical behavior of a dynamical system and the interpretation of such behavior as carrying out inference. It blurs the boundary between the ontological mode of the system of interest and the epistemological significance it acquires through its dynamic interaction with the environment. New materialism (or neo-materialism), despite lacking a single definition, refers to a range of emerging perspectives that attempt to dismantle the long-held divisions between ontology, epistemology, and even ethics, with the aim of achieving a comprehensive transformation of naturalized thinking. In this context, new materialism provides powerful tools to reframe some of the conceptual foundations of the FEP. This paper is the first in a series that aims to systematically construct a neo-materialistic perspective for the FEP, exploring its wide-ranging implications. It serves as an introduction to the series, arguing for the justification of deploying new materialism to reframe the FEP and introducing some essential concepts to be utilized in developing a neo-materialistic account of the FEP.

The spread of ideas is a fundamental concern of today’s news ecology. Understanding the dynamics of the spread of information and its co-option by interested parties is of critical importance. Research on this topic has shown that individuals tend to cluster in echo-chambers and are driven by confirmation bias. In this paper, we leverage the active inference framework to provide an in silico model of confirmation bias and its effect on echo-chamber formation. We build a model based on active inference, where agents tend to sample information in order to justify their own view of reality, which eventually leads to them to have a high degree of certainty about their own beliefs. We show that, once agents have reached a certain level of certainty about their beliefs, it becomes very difficult to get them to change their views. This system of self-confirming beliefs is upheld and reinforced by the evolving relationship between agent's beliefs and its observations, which over time will continue to provide evidence for their ingrained ideas about the world. The epistemic communities that are consolidated by these shared beliefs, in turn, tend to produce perceptions of reality that reinforce those shared beliefs. We provide an active inference account of this community formation mechanism. We postulate that agents are driven by the epistemic value that they obtain from sampling or observing the behaviors of other agents. Inspired by digital social networks like Twitter, we build a generative model in which agents generate observable social claims or posts (e.g. `tweets') while reading the socially-observable claims of other agents, that lend support towards one of two mutually-exclusive abstract topics. Agents can choose which other agent they pay attention to at each timestep, and crucially who they attend to and what they choose to read influences their beliefs about the world. Agents also assess their local network’s perspective, influencing which kinds of posts they expect to see other agents making. The model was built and simulated simulated using the freely-available Python package pymdp. The proposed active inference model can reproduce the formation of echo-chambers over social networks, and gives us insight into the cognitive processes that lead to this phenomenon.

Probabilistic inference problems have very broad practical applications. To solve this kind of problems under conditions of certainty, an effective mathematical apparatus has been developed. In real situations, obtaining deterministic estimates of relevant probabilities is often difficult; therefore, problems with handling uncertain estimates of probabilities appear. This paper examines the problem of probabilistic inference with probability trees provided that the initial probabilities are given in the form of intervals of their possible values.

A general framework for inference in dynamical systems is described, based on the language of Bayesian probability theory and making use of the maximum entropy principle. Taking as fundamental the concept of a path, the continuity equation and Cauchy's equation for fluid dynamics arise naturally, while the specific information about the system can be included using the Maximum Caliber (or maximum path entropy) principle.

Machine learning forks into three main branches such as supervised learning, unsupervised learning, and reinforcement learning where reinforcement learning is much potential to artificial intelligence (AI) applications because it solves real problems by progressive process in which possible solutions are improved and finetuned continuously. The progressive approach, which reflects ability of adaptation, is appropriate to the real world where most events occur and change continuously and unexpectedly. Moreover, data is getting too huge for supervised learning and unsupervised learning to draw valuable knowledge from such huge data at one time. Bayesian optimization (BO) models an optimization problem as a probabilistic form called surrogate model and then directly maximizes an acquisition function created from such surrogate model in order to maximize implicitly and indirectly the target function for finding out solution of the optimization problem. A popular surrogate model is Gaussian process regression model. The process of maximizing acquisition function is based on updating posterior probability of surrogate model repeatedly, which is improved after every iteration. Taking advantages of acquisition function or utility function is also common in decision theory but the semantic meaning behind BO is that BO solves problems by progressive and adaptive approach via updating surrogate model from a small piece of data at each time, according to ideology of reinforcement learning. Undoubtedly, BO is a reinforcement learning algorithm with many potential applications and thus it is surveyed in this research with attention to its mathematical ideas. Moreover, the solution of optimization problem is important to not only applied mathematics but also AI.

Bootstrap resampling techinques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional φ(F), where F is a random distribution function. Efron’s and Rubin’s bootstrap procedures can be extended introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e. bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data.

Carbon Capture and Storage (CCS) stands as a pivotal technological stride toward a sustainable future, with the practice of injecting supercritical CO2 into subsurface formations having already been an established practice for enhanced oil recovery operations. The overarching objective of CCS is to protract the operational viability and sustainability of platforms and oilfields, thereby facilitating a seamless transition towards sustainable practices. This study introduces a comprehensive framework for optimizing well placements in CCS operations, employing a derivative-free method known as Bayesian optimization. The development plan is tailored for scenarios featuring aquifers devoid of flow boundaries, incorporating production wells tasked with controlling pressure buildup and injection wells dedicated to CO2 sequestration. Notably, the wells operate under group control, signifying predefined injection and production targets and constraints that must be adhered to throughout the project’s lifespan. As a result, the objective function remains invariant under specific permutations of the well locations. Our investigation delves into the efficacy of Bayesian optimization under the introduced permutation invariance. The results reveal that it demonstrates critical efficiency in handling the optimization task extremely fast. In essence, this study advocates for the efficacy of Bayesian optimization in the context of optimizing well placements for CCS operations, emphasizing its potential as a preferred methodology for enhancing sustainability in the energy sector.

We present a Deep Learning generative model specialized to work with graphs with a regular geometry. It is build on a Variational Autoencoder framework and employs Graph convolutional layers in both encoding and decoding phases. We also introduce a pooling technique (ReNN-Pool), used in the encoder, that allows to downsample graph nodes in a spatially uniform and highly interpretable way. In the decoder, a symmetrical un-pooling technique is used to retrieve the original dimensionality of graphs. Performance of the model are tested on the standard Sprite benchmark dataset, a set of 2D images of video game characters, adequately transforming images data into graphs, and on the more realistic use-case of a dataset of cylindrical-shaped graph data that describe the distributions of the energy deposited by a particle beam in a medium.

We present a method to improve the reconstruction and generation performance of variational autoencoder (VAE) by injecting an adversarial learning. On the other hand, instead of comparing the reconstructed with the original data to calculate the reconstruction loss, we use a consistency principle for deep features. The training process of the VAE is then divided into two steps, training the encoder and then training the decoder. By using this two-step learning process, our method can be more widely used in applications other than image processing. While training the encoder, the label information is integrated to better structure the latent space in a supervised way. The adversarial constraints allow the decoder to generate data with better authenticity and more realistic than the conventional VAE. We present experimental results to show that our method gives better performance than the original VAE.

Generative artificial intelligence (GenAI) has been developing with many incredible achievements like ChatGPT and Bard. Deep generative model (DGM) is a branch of GenAI, which is preeminent in generating raster data such as image and sound due to strong points of deep neural network (DNN) in inference and recognition. The built-in inference mechanism of DNN, which simulates and aims to synaptic plasticity of human neuron network, fosters generation ability of DGM which produces surprised results with support of statistical flexibility. Two popular approaches in DGM are Variational Autoencoders (VAE) and Generative Adversarial Network (GAN). Both VAE and GAN have their own strong points although they share and imply underline theory of statistics as well as incredible complex via hidden layers of DNN when DNN becomes effective encoding/decoding functions without concrete specifications. In this research, VAE and GAN is unified into a consistent and consolidated model called Adversarial Variational Autoencoders (AVA) in which VAE and GAN complement each other, for instance, VAE is good at generator by encoding data via excellent ideology of Kullback-Leibler divergence and GAN is a significantly important method to assess reliability of data which is realistic or fake. In other words, AVA aims to improve accuracy of generative models, besides AVA extends function of simple generative models. In methodology this research focuses on combination of applied mathematical concepts and skillful techniques of computer programming in order to implement and solve complicated problems as simply as possible.

In this paper, our goal is to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate $\eta$-convexity conditions for locally Lipschitzian functions

Gradient-domain image processing is a technique where, instead of operating directly on the image pixel values, the gradient of the image is computed and processed. The resulting image is obtained by reintegrating the processed gradient. This is normally done by solving the Poisson equation, most oftenly by means of a finite difference implementation of the gradient descent method. However, this technique in some cases lead to severe haloing artefacts in the resulting image. To deal with this, local or anisotropic diffusion has been added as an ad-hoc modification of the Poisson equation. In this paper, we show that a version of anisotropic gradient-domain image processing can result from a more general variational formulation through the minimisation of a functional formulated in terms of the eigenvalues of the structure tensor of the differences between the processed gradient and the gradient of the original image. Example applications of linear and non-linear local contrast enhancement and colour image daltonisation illustrate the behaviour of the method.

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

In this article we introduce an extension of the Akash distribution. We use the slash 1 methodology to make the kurtosis of the Akash distribution more flexible. We study the general 2 density of this new distribution, some properties, moments, coefficients of asymmetry and kurtosis. 3 Statistical inference is performed using the methods of moments and maximum likelihood via the 4 EM algorithm. A simulation study is carried out to observe the behavior of the maximum likelihood 5 estimator. An application to a real data set with high kurtosis is considered, where it is shown that 6 the new distribution fits better than other extensions of the Akash distribution.

In this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals. We begin with an overview of Husserlian phenomenology, focusing on aspects of inner time consciousness, namely, retention, primal impression, and protention. We then review active inference as a formal approach to modeling agent behavior, based on variational (approximate Bayesian) inference. Expanding upon Husserl’s model of time consciousness, we consider collective goal-directed behavior, emphasizing shared protentions among agents and their connection to the shared generative models of active inference. This integrated framework aims to formalize shared goals in terms of shared protentions, and to thereby shed light on the emergence of group intentionality. Building on this foundation, we incorporate mathematical tools from category theory; particularly, sheaf and topos theory, to furnish a mathematical image of individual and group interactions within a stochastic environment. Specifically, we employ morphisms between polynomial representations of individual agent models, allowing predictions not only of their own behaviors but also those of other agents and environmental responses. Sheaf and topos theory facilitate the construction of coherent agent worldviews and provides a way of representing consensus or shared understanding. We explore the emergence of shared protentions, bridging the phenomenology of temporal structure, multi-agent active inference systems, and category theory. Shared protentions are highlighted as pivotal for coordination and achieving common objectives. We conclude by acknowledging the intricacies stemming from stochastic systems and uncertainties in realizing shared goals.

The mutual information between the state of a neural network and the state of the external world represents the amount of information stored in the neural network that is associated with the external world. In contrast, the surprise of the sensory input indicates the unpredictability of the current input. In other words, this is a measure of inference ability, and an upper bound of the surprise is known as the variational free energy. According to the free-energy principle (FEP), a neural network continuously minimizes the free energy to perceive the external world. For the survival of animals, inference ability is considered to be more important than simply memorized information. In this study, the free energy is shown to represent the gap between the amount of information stored in the neural network and that available for inference. This concept involves both the FEP and the infomax principle, and will be a useful measure for quantifying the amount of information available for inference.

Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role for extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data, to 2-D image data, to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results.

We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on QUBO (quadratic unconstrained binary optimization) problems, which are well-suited for qubit superposition states. Specifically, we demonstrate circuit designs which encode QUBOs as ‘cost oracle’ operations UC, which when combined with the standard Grover diffusion operator Us lead to high probabilities of measurement for states corresponding to the optimal and near optimal solutions. In order to achieve these probabilities, a single scalar parameter ps is required, which we show can be found through a variational quantum-classical hybrid approach.

As a fast and nondestructive spectroscopic analysis technique, Raman spectroscopy has been widely applied in chemistry. However, noise is usually unavoidable in Raman spectra. Hence, denoising is an important step before Raman spectral analysis. A novel spectral denoising method based on variational mode decomposition (VMD) was introduced to solve the above problem. The spectrum is decomposed into a series of modes (uk) by VMD. Then, the high frequency noise modes are removed and the remaining modes are reconstructed to obtain the denoised spectrum. The proposed method was verified by two artificial noised signals and two actual Raman spectra. As comparison, empirical mode decomposition (EMD), Savitzky-Golay (SG) smoothing and discrete wavelet transformation (DWT) are also investigated. At the same time, signal-to-noise ratio (SNR) was introduced as evaluation indicators to verify the performance of the proposed method. The results show that compared with EMD, VMD can significantly improve mode mixing and endpoint effect. Some information of the small sharp peak is lost after VMD denoising. However, VMD lost fewer information than that of EMD, SG smoothing and DWT. Moreover, the Raman spectrum by VMD denoising is more excellent than that of EMD, SG smoothing and DWT in terms of visualization and SNR. Therefore, VMD provides superior denoising capabilities for Raman spectra.

Phylogenomics has enriched our understanding that the Tree of Life can have network-like or reticulate structures among some taxa and genes. Non-vertical modes of evolution—such as hybridization/introgression and horizontal gene transfer—deviate from a strictly bifurcating tree model, causing non-treelike patterns. Here, we present a brief overview of a phylogenomic workflow for inferring organismal histories and compare methods for detecting reticulate evolution. We discuss how the timing of coalescent events can help disentangle introgression from incomplete lineage sorting and how horizontal gene transfer events can help determine the relative timing of speciation events. In doing so, we identify pitfalls of certain methods and discuss how to extend their utility across the Tree of Life. Workflows, methods, and future directions discussed herein underscore the need to embrace reticulate evolutionary patterns for understanding the timing and rates of evolutionary events, providing a clearer understanding of life’s history.

Coastal marine ecosystems worldwide, like Florida Bay, are increasingly affected by tide alteration and anthropogenic disturbances which affect water quality imbalance leading to algal blooms. Increased bloom persistence is a serious threat due to the long-lasting impact on processes like carbon cycle and services like species presence. However, exploring eco-environmental feedback patterns of algal blooms remains challenging and poorly investigated, also due to the paucity of data. Florida Bay, taken as an epitome, has long experienced algal blooms in its central and western regions, and in 2006 an unprecedented bloom occurred in the eastern habitats. We analyzed the occurrence of blooms from three perspectives: (1) the spatial spreading networks of chlorophyll-a (CHLa) that pinpoints source and unbalanced habitats; (2) the fluctuations of water quality factors pre- and post-bloom outbreaks to in assess environmental impacts of ecological dysbiosis and target prevention and control of algal of blooms; and (3) the biogeochemical-spreading network topological co-evolution to quantify ecosystemic stability and ecological shift likelihood in long-term. Here, we propose Transfer Entropy (TE) to quantify dynamical interactions between spatial areas and biogeochemical factors (ecosystem connectome) underpinning bloom emergence and spreading, as well as environmental effects; the Pareto principle is defined for identifying the salient eco-environmental interactions of CHLa. We quantified the spatial dynamics of algal blooms, and thus obtained areas in need for ecological monitoring and potential bloom control. Results show that algal blooms are increasingly persistent over space with long-term negative effects on water quality factor. A dichotomy is reported between spatial ecological corridors of spreading and biogeochemical networks as well as divergence from the optimal eco-organization: randomization of the former due to nutrients' overload and temperature increase leads to scale-free CHLa spreading and extreme outbreaks a posteriori. Subsequently this increases bloom persistence, turbidity and salinity with potentially strong ecological effects on highly biodiverse and vulnerable areas such as tidal flats and marshes. Algal blooms are important ecosystem regulators of nutrient cycles; however, beyond limit chlorophyll-a outbreaks cause aquatic species mortality due to their effect on water turbidity, nutrient balance (nitrogen and phosphorus in particular), salinity and temperature. Beyond compromising local environmental quality, socio-ecological services are also compromised at large scales, yet ecological assessment models like the one presented are in need of application in subtropical and tropical bays worldwide.

In recent years, large language models have demonstrated remarkable performance across various natural language processing (NLP) tasks. However, deploying these models for real-world applications often requires efficient inference solutions to handle the computational demands. In this paper, we explore the utilization of CPUs for accelerating the inference of large language models. Specifically, we introduce a parallelized approach to enhance throughput by 1) Exploiting the parallel processing capabilities of modern CPU architectures, 2) Batching the inference request. Our evaluation shows the accelerated inference engine gives an 18-22x improvement in the generated token per sec. The improvement is more with longer sequence and larger models. In addition to this, we can also run multiple workers in the same machine with NUMA node isolation to further improvement in tokens/s. Table 2, we have received 4x additional improvement with 4 workers. This would also make Gen-AI based products and companies’ environment friendly, our estimates shows that CPU usage for Inference could reduce the power consumption of LLMs by 48.9% (1252 W for A100 with AMD EPYC 7V13 vs 613 W for Intel® Xeon® Gold 6538N) while providing production ready throughput & latency.

In this paper, we shall introduce the interval-valued spatial error model. Based on the idea of least square method of single-valued case, we give the parameter estimator for interval-valued spatial error model. The theoretical properties of the proposed estimator are proved. Finally, we give the numerical analysis and a real example.

This paper focuses on a joint model to analyse longitudinal proportion and survival data. After transforming the longitudinal proportional data by a logit function, we adopt a partially linear mixed-effect model for it, in which nonlinear function of time is fitted via using B-splines technique and a centered Dirichlet Process Mixture Model (CDPMM) is specified for a general distribution of random effects. The survival data is assumed to a Cox proportional hazard model, the sharing random effects joint model is developed for the two types of data. Combining the Gibbs sampler and the Metropolis-Hastings algorithm, we propose a Bayesian Lasso (BLasso) method to simultaneously estimate unknown parameters and select important covariates. Simulation studies are conducted to investigate the finite sample performance of the proposed methods. An example from the MA.5 research experiment is used to illustrate the proposed methodologies.

In this paper study, we develop a Bayesian Network model selection principle that address addresses the incommensurability of network features obtained from incongruous datasets and overcomes performance irregularities of the Minimum Description Length model selection principle. This is achieved (i) by approaching model evaluation as a classification problem, (ii) by estimating the effect that sampling error has on the satisfiability of conditional independence criterion, as reflected by Mutual Information, and (iii) by utilizing this error estimate to penalize uncertainty in the Minimum Uncertainty (MU) model selection principle. We validate our findings numerically and demonstrate the performance advantages of the MU criterion. Finally, we illustrate the advantages of the new model evaluation framework on a tRNA structural biology example.

The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

We present a first formal analysis of specific and complete local integration. Complete local integration was previously proposed as a criterion for detecting entities or wholes in distributed dynamical systems. Such entities in turn were conceived to form the basis of a theory of emergence of agents within dynamical systems. Here, we give a more thorough account of the underlying formal measures. The main contribution is the disintegration theorem which reveals a special role of completely locally integrated patterns (what we call ι-entities) within the trajectories they occur in. Apart from proving this theorem we introduce the disintegration hierarchy and its refinement-free version as a way to structure the patterns in a trajectory. Furthermore we construct the least upper bound and provide a candidate for the greatest lower bound of specific local integration. Finally, we calculate the i-entities in small example systems as a first sanity check and find that ι-entities largely fulfil simple expectations.

The human-readable simplicity with which the CSV format was devised, together with the absence of a standard that strictly defines this format, has allowed the proliferation of several variants in the dialects with which these files are written. The latter has meant that the exchange of information between data management systems, or between countries and regions, requires human intervention during the data mining and cleansing process. This has led to the development of various computational tools that aim to accurately determine the dialects of CSV files, in order to avoid data loss at data loading stage in a given system. However, the dialect detection is a complex problem and current systems have limitations or make assumptions that need to be improved and/or extended. This paper proposes a method for determining CSV file dialects through table uniformity, a statistical approach based on table consistency and records dispersion measurement along with the detection of data type over each field. The new method has a 100\% accuracy on a dataset with 148 CSV files composed of samples coming from a data load testing framework and some others added as verification of the parsing routines. In tests on truly messy data, the proposed solution outperforms the state-of-the-art tool by achieving an improvement of about 10\% in the accuracy with which dialects are detected. Furthermore, the proposed method is accurate enough to determine dialects by reading only ten records, requiring more data to disambiguate those cases where the first records do not contain the necessary information to conclude with a dialect determination.

We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink energy, the energy of valence fermions and the fermion vacuum polarization energy. The latter arises from the interaction of the kink with the Dirac sea and is required for consistency of the semi-classical expansion for the fermions. Earlier studies only considered the valence part and observed a substantial back-reaction. This was reflected by a sizable distortion of the kink profile. We find that this distortion is strongly mitigated when the Dirac sea is properly accounted for. As a result the back-reaction merely produces a slight squeeze or stretch of the kink profile.

Despite the importance of few-shot learning, the lack of labeled training data in the real world, makes it extremely challenging for existing machine learning methods as this limited data set does not represent the data variance well. In this research, we suggest employing a generative approach using variational autoencoders (VAEs), which can be used specifically to optimize few-shot learning tasks by generating new samples with more intra-class variations. The purpose of our research is to increase the size of the training data set using various methods to improve the accuracy and robustness of the few-shot face recognition. Specifically, we employ the VAE generator to increase the size of the training data set, including the basic and the novel sets while utilizing transfer learning as the backend. Based on extensive experimental research, we analyze various data augmentation methods to observe how each method affects the accuracy of face recognition. We conclude that the face generation method we proposed can effectively improve the recognition accuracy rate to 96.47% using both the base and the novel sets.

We present a formalism to assess the safety of the COVID19 vaccines and infer a causal relation between vaccine administration and adverse effects, in particular death. We use data on adverse effects from VAERS covering the time interval [01-10-2020, 31-12-2021] (downloaded on 1 Feb 2022). We measure a vaccine fatality rate of order 0.01 for all vaccine manufacturers and identify a strong heterogeneity in the vaccine toxicity across vaccine lots, spanning up to four orders of magnitude. We compute the correlation between vaccination dates and death dates, and produce an estimate of the time lag that maximises the correlation, finding that the onset of adverse effects happened statistically (i.e. 32-41 percentiles) within one day after the vaccine administration and that death happened statistically (i.e. 22-50 percentiles) within about two weeks after the vaccine administration. These results provide data-based insights that can guide public health measures and health insurance policies.

The effectiveness of Fuzzy Inference Systems (FISs) in manipulating uncertainty and nonlinearity makes them a subject of significant interest for decision-making in embedded systems. Accordingly, optimizing FIS hardware improves its performance, efficiency, and capabilities, leading to a better user experience, increased productivity, and cost savings. To be compatible with the limited power budget in most embedded systems, this paper presents a framework to realize ultra-low power FIS hardware. It supports optimizations for both conventional arithmetic as well as MSDF-computing to be highly consistent with MSDF-based sensors. In MSDF-computing FIS all the processes of fuzzification, inference, and defuzzification are done on serially coming data bits. To demonstrate the efficiency of the proposed framework, we utilized Matlab, Chisel3, and Vivado to implement it from high-level descriptions of FIS to hardware synthesis. We also developed a Scala library in Chisel3 to establish a connection between these tools, bridging the gap, and facilitating design space exploration at the arithmetic level. Furthermore, we realized an FIS for the navigation of autonomous mobile robots in unknown environments. Synthesis results show the superiority of the output of our suggested design framework in terms of resource usage as well as power and energy consumption compared to the Matlab HDL code generator output.

Safety is very important in aviation since a loss of safety frequently results in both fatalities and financially damaging situations that are typically unrecoverable. Thus, achieving safety as much as possible is the primary goal of practically all aviation technology work. In this study, an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based classifier is created to estimate the fault risk factor of airplanes. Five categories of real fleet data belonging to structure, electrical, avionic, motor systems, and incident statistics of the planes have been used for classifier development. A risk factor determination for each plane is the output of the developed intelligent classifier, and it can be used to identify general overhaul candidate planes and stop defects and crashes before they happen. The obtained results show that using ANFIS provides a great capability in processing many inputs and outputs depending on different types and classes in the aviation industry and thus predicting the failure risk of the airplane efficiently.

The increasing prevalence of species that are detrimental to biodiversity is a major concern, particularly for managers of National Parks. To develop effective programs for controlling weeds, it is essential to have a thorough understanding of the extent and severity of infestations, as well as the contributing factors such as temperature, rainfall, and disturbance. Predicting these factors on a regional scale requires models that can incorporate a wide range of variables in a quantifiable manner, while also assisting with on-ground operations. In this study, we present two Bayesian Network models specifically designed for six significant weed species found along the southern coast of Australia. Our models are based on empirical data collected during a coastal weed survey conducted in 2015 and repeated in 2016. We applied these models to the coastal national parks in the isolated and pristine East Gippsland region. Importantly, the prediction models were developed at two different spatial scales that directly corresponded to the scale of the observations. Our findings indicate that coastal habitats, with their vulnerable environments and prevalence of open dune systems, are particularly susceptible to weed infestations. Moreover, adjacent regions also have the potential for colonization if these infestations are not effectively controlled. Climate-related factors play a role in moderating the potential for colonization, which is a significant concern for weed control efforts in the context of global climate change.

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure, alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the actual estimation of the noise power. A complete Bayesian study over the model parameters and the scale parameter can be also performed. Numerical experiments show the benefits of the proposed approach.

This paper considers estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the Log--Huber loss function which is resistant to outliers and useful to find robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of Bayesian risk function with themselves as well as the usual plug-in density ratio estimators. Some applications such as classification and divergence function estimation are addressed.

Technology development changes society and society demands new and innovative technology development. We analyze technology to understand society and technology itself. Many researches have been introduced in various fields. Most of them were about patent analysis. This is because detailed and accurate results of research and development are patented. In this paper, we study on new patent analysis method based on count data model and Bayesian regression analysis. Using count data model, we analyze the technological keywords extracted from the collected patent documents. We use the posterior distribution of Bayesian statistics to reflect the experience and knowledge of the relevant technological experts in the analysis model. Moreover, we apply the proposed model to finding sustainable technologies. Finding and developing sustainable technologies is an important activity for companies and research institutes to maintain their technological competitiveness. To illustrate how our modeling could be applied to real domain, we carry out a case study using the patent documents related to artificial intelligence.

This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty's motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty, and show that under certain conditions on p, the unique equilibrium is one where the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. Finally, we show that our formulation can explain the experimental results in Page (1998) [12]; that more people gradually choose switch as the number of doors in the problem increases.

Categorical variables are common in spatial data analysis. Traditional analytical methods for deriving probabilities of class occurrence, such as kriging-family algorithms, have been hindered by the discrete characteristics of categorical fields. This study introduces the theoretical backgrounds of linear Bayesian updating (LBU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to present the solid theoretical foundations of LBU and provide a categorical random field prediction method which yields relatively higher classification accuracy compared with conventional Markov chain random field (MCRF) approach. A real-world case study has also been carried out to demonstrate the superiority of our method. Since the LBU idea is originated from aggregating expert opinions and not restricted to conditional independent assumption (CIA), it may prove to be reasonably adequate for analyzing complex geospatial data sets, like remote sensing images or area-class maps.

In recent years, Edge Intelligence (EI) has emerged, combining edge computing with AI, specifically deep learning, to run AI algorithms directly on edge devices. In practical applications, EI faces challenges related to computational power, power consumption, size, and cost, with the primary challenge being the trade-off between computational power and power consumption. This has rendered traditional computing platforms unsustainable, making heterogeneous parallel computing platforms a crucial pathway for implementing EI. In our research, we leveraged the Xilinx Zynq 7000 heterogeneous computing platform, employed High-Level Synthesis (HLS) for design, and implemented two different accelerators for LeNet-5 using loop unrolling and pipelining optimization techniques. The experimental results show that when running at a clock speed of 100 MHz, the PIPELINE accelerator, compared to the UNROLL accelerator, experiences an 8.09% increase in power consumption but speeds up by 14.972 times, making the PIPELINE accelerator superior in performance. Compared to the CPU, the PIPELINE accelerator reduces power consumption by 91.37% and speeds up by 70.387 times, while compared to the GPU, it reduces power consumption by 93.35%.This study provides two different optimization schemes for edge intelligence applications through design and experimentation, and demonstrates the impact of different quantization methods on FPGA resource consumption. These experimental results can provide a reference for practical applications, thereby providing a reference hardware acceleration scheme for edge intelligence applications.

This work presents significant results obtained by the application of global optimization techniques to the design of finite, normal form games with mixed strategies. To that end, the Fuzzy ASA global optimization method is applied to several design examples of strategic games, demonstrating its effectiveness in obtaining payoff functions whose corresponding games present a previously established Nash equilibrium. In other words, the game designer becomes able to choose a convenient Nash equilibrium for a generic finite state strategic game and the proposed method computes payoff functions that will realize the desired equilibrium, making it possible for the players to reach the favorable conditions represented by the chosen equilibrium. Considering that game theory is a very significant approach for modeling interactions between competing agents, and Nash equilibrium represents a powerful solution concept, portraying situations in which joint strategies are optimal in the sense that players cannot benefit from individually modifying their current strategies provided that other players do not change their strategies as well, it is natural to infer that the proposed method may be very useful for strategists in general. In summary, it is a genuine instance of artificial inference of payoff functions after a process of global machine learning, applied to their numerical components.

We prove a quasi-pseudometric version of the strong Ekeland principle proved by P. Georgiev and T. Suzuki.

In the era of big data with increasingly complex data structures and ever-larger data scales, matrix-type data are becoming highly valued and their applications in the fields of medicine, industry, education, geography, and astronomy are growing in extent. In recent years, significant progress has been made in the practical use of matrix variable t-distribution finite mixture models for handling data in order to address the issues of multi-subgroup structures and long data tails. In this paper, the expectation-maximization (EM) algorithm with penalized maximum likelihood is proposed to resolve the problem of the unbounded nature of the likelihood function applied to the model by considering the degeneracy of the variance-covariance matrix of this model. Our data were analyzed through simulations and real data, and the results demonstrate that our model is effective in both preventing the likelihood function from being unbounded and in ensuring the accuracy of the estimated parameters of the EM algorithm.

Computer systems are involved in many critical human applications today, so that a small error can lead to serious and dangerous problems. These errors can be from an error in the incorrect design of the user interface to an error in the program code. The success of a software product depends on several factors. Given that different organizations and institutions use software products, the need to have a quality and desirable Software according to the goals and needs of the organization makes measuring the quality of software products. an important issue for most organizations and institutions, To be sure of having the right software. It is necessary to use a standard quality model to examine the features and sub-features for a detailed and principled study in the quality discussion. In this study, the quality of Word software was measured by Adaptive Neural Fuzzy Inference System. In recent years, powerful systems called fuzzy inference systems on The basis of adaptive neural network (ANFIS) has been used in various sciences. Using the power of neural network training and the linguistic advantage of fuzzy systems, these types of systems have been able to realize the advantages of the two in terms of analyzing very powerful complex processes. Considering the importance of software quality and to have a good and usable software in terms of quality and measuring the quality of software during the study. It was applied at different levels to make the result of measuring the quality of Word software more accurate and closer to reality. In this research, the quality of the software product is measured based on the adaptive neural-fuzzy inference system in ISO standard. According to the results obtained in this study, it is understood that quality is a continuous and hierarchical concept and the quality of each part of the software at any stage of production can lead to high quality products.

The maximization of entropy S within a closed system is accepted as an inevitability (as the second law of thermodynamics) by statistical inference alone. The Maximum Entropy Production Principle (MEPP) states that not only S maximizes, but $\dot{S}$ as well: a system will dissipate as fast as possible. There is still no consensus on the general validity of this MEPP, even though it shows remarkable explanatory power (both qualitatively and quantitatively), and has been empirically demonstrated for many domains. In this theoretical paper I provide a generalization of entropy gradients, to show that the MEPP actually follows from the same statistical inference, as that of the 2nd law of thermodynamics. For this generalization I only use the concepts of super-statespaces and microstate-density. These concepts also allow for the abstraction of 'Self Organizing Criticality' to a bifurcating local difference in this density, and allow for a generalization of the fundamentally unresolved concepts of 'chaos' and 'order'.

Medical insurance claims are becoming increasingly common data sources to answer a variety of questions in biomedical research. Although comprehensive in terms of longitudinal characterization of disease development and progression for a potentially large number of patients, population-based studies using these datasets require thoughtful modification to sample selection and analytic strategies, relative to other types of studies. Along with complex selection bias and missing data issues, claims-based studies are purely observational, which limits effective understanding and characterization of the treatment differences between groups being compared. All these issues contribute to a crisis in reproducibility and replication of comparative findings. This paper offers some practical guidance to the full analytical process, demonstrates methods for estimating causal treatment effects on several types of outcomes common to such studies, such as binary, count, time to event and longitudinally varying repeated measures outcomes, and aims to increase transparency and reproducibility. We provide an online version of the paper with readily implementable code for the entire analysis pipeline to serve as a guided tutorial for practitioners. The online version can be accessed at https://rydaro.github.io/. The analytic pipeline is illustrated using a sub-cohort of patients with advanced prostate cancer from the large Clinformatics TM Data Mart Database (OptumInsight, Eden Prairie, Minnesota), consisting of 73 million distinct private payer insurees from 2001-2016.

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

Bayesian nonlinear mixed effects models for data in the form of continuous, repeated measurements from a population, also known as Bayesian hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual specific characteristics and relevant uncertainty quantification. Due to the limitation of computational power, this framework was relatively dormant until the late 1980s, but in recent years, the statistical research community saw vigorous development of new methodological and computational techniques for these models, the emergence of software, and wide application of the models in numerous industrial and academic fields. This article presents an overview of the formulation, interpretation, and implementation of Bayesian nonlinear mixed effects models and surveys recent advances and applications.

Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning.

In recent decades, the Variational AutoEncoder (VAE) model has shown good potential and capabilities in image generation and dimensionality reduction. The combination of VAE and various machine learning frameworks has also worked effectively in different daily life applications, however its possibility and effectiveness in modern game design has seldom been explored nor assessed. The use of its feature extractor for data clustering was minimally discussed in literature neither. This paper first attempts to explore different mathematical properties of the VAE model, in particular, the theoretical framework of the encoding and decoding processes, the possible achievable lower bound and loss functions of different applications; then applies the established VAE model into generating new game levels within two well-known game settings; as well as validating the effectiveness of its data clustering mechanism with the aid of the Modified National Institute of Standards and Technology (MNIST) database. Respective statistical metrics and assessments were also utilized for evaluating the performance of the proposed VAE model in aforementioned case studies. Based on the statistical and spatial results, several potential drawbacks and future enhancement of the established model were outlined, with the aim of maximizing the strengths and advantages of VAE for future game design tasks and relevant industrial missions.

This study examines the causal relationships between interest rates in the Korean financial market using a vector error correction model (VECM) and a Bayesian network. The Bayesian network, a novel approach in this context, identifies two distinct transmission channels: one led by call rates (reflecting monetary policy) and another by 10-year Treasury bond yields (reflecting fiscal policy). While the call rate channel aligns with traditional views, affecting bank lending rates, corporate bond spreads, and commercial paper rates, the 10-year Treasury yield channel highlights a separate fiscal policy transmission mechanism, influencing commercial paper rates indirectly through 30-year Treasury yields and directly impacting merchant bank lending rates. This finding suggests that fiscal intervention could potentially interfere with monetary policy, emphasizing the need for coordinated macroeconomic policy measures. The study also emphasizes the role of 10-year Treasury bonds as a benchmark in the Korean bond market, reflecting medium- to long-term economic outlooks and serving as the underlying asset for various derivatives.

Oral squamous cell carcinoma often arises from an oral potentially malignant disorder called oral leukoplakia (OL). With this work we aimed to develop a novel data-driven predictive model based on gene expression profiles to distinguish OL patients who underwent malignant transformation from those who did not. We used the Tree Augmented Naïve (TAN) Bayes classifier to predict the posterior probability of having oral cancer given the data. 86 patients were included with a median follow-up of 7.11 years. Fifty-one patients (51/86; 59%) underwent malignant transformation. We found that 16 genes were predictors of oral cancer in patients with OL and these included SLC7A11, SPINK6, SERPINA12, VIT, ATP1B3, CST6, FLRT2, ELMOD1, AZGP1, RNASE13, DIO2, ECM1, CYP4F11, SYTL4, AKR1C1, and AKR1C3. In conclusion, we showed that Bayesian gene networks are a data-driven approach which could be used also in other predictor models in oncology.

Lysine is the first limiting essential amino acid in rice because it is present in the lowest quantity compared to all the other amino acids. Amino acids are the building block of proteins and play an essential role in maintaining the human body’s healthy functioning. Rice is a staple food for large proportion of the global population, thus increasing the lysine content in rice will improve its nutritional value. In this paper, we studied the lysine biosynthesis pathway in rice (Oryza Sativa) to identify the regulators of the lysine reporter gene LYSA (LOC_Os02g24354). Genetically intervening at the regulators has the potential to increase the overall lysine content in rice. We modeled the lysine biosynthesis pathway in rice seedlings under normal and saline (NaCl) stress conditions using Bayesian networks. We estimated the model parameters using experimental data and identified the gene DAPF(LOC_Os12g37960) as a positive regulator of the lysine reporter gene LYSA under both normal and saline stress conditions. Based on this analysis, we conclude that the gene DAPF is a potent candidate for genetic intervention. Upregulating DAPF using methods such as CRISPR-Cas9 has the potential to upregulate the lysine reporter gene LYSA and increase the overall lysine content in rice.

The ability to smell is crucial for most species as it enables the detection of environmental threats like smoke, fosters social interactions, and contributes to the sensory evaluation of food and eating behavior. The high prevalence of smell disturbances throughout the life span calls for a continuous effort to improve tools for quick and reliable assessment of olfactory function. Odor-dispensing pens, called Sniffin' Sticks, are an established method to deliver olfactory stimuli during diagnostic evaluation. We tested the suitability of a Bayesian adaptive algorithm (QUEST) to estimate olfactory sensitivity using Sniffin' Sticks by comparing QUEST sensitivity thresholds with those obtained using a procedure based on an established standard staircase protocol. Thresholds were measured twice with both procedures in two sessions (Test and Retest). Overall, both procedures exhibited considerable overlap with QUEST displaying slightly higher test-retest correlations, less variability between measurements, and reduced testing duration. Notably, participants were more frequently presented with the highest concentration during the QUEST which may foster adaptation and habituation effects. We conclude that further research is required to better understand and optimize the procedure for assessment of olfactory performance.

Reliable quantification of pulmonary arterial pressure is essential in the diagnostic and prognostic assessment of a range of cardiovascular pathologies including rheumatic heart disease, yet an accurate and routinely available method for its quantification remains elusive. This work proposes an approach to infer pulmonary arterial pressure based on scientific machine learning techniques and non-invasive, clinically available measurements. A 0-D multicompartment model of the cardiovascular system was optimized using several optimization algorithms, subject to forward-mode automatic differentiation. Measurement data were synthesized from known parameters to represent the healthy, mitral regurgitant, aortic stenosed and combined valvular disease situations with and without pulmonary hypertension. Eleven model parameters were selected for optimization based on 95 % explained variation in mean pulmonary arterial pressure. A hybrid Adam and limited-memory Broyden-Fletcher-Goldfarb-Shanno optimizer yielded the best results with input data including valvular flow rates, heart chamber volume changes and systematic arterial pressure. Mean absolute percentage errors ranged from 1.8 % to 3.78 % over the simulated test cases. The model was able to capture pressure dynamics under hypertensive conditions with pulmonary arterial systole, diastole, and mean pressure average percentage errors of 1.12 %, 2.49 % and 2.14 %, respectively. The relatively low errors highlight the potential of the proposed model to recover pulmonary pressures for diseased heart valve and pulmonary hypertensive conditions.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy.” Upper and lower error bars on the accuracy are provided by the arithmetic mean and the -2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the -2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and -2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the -2/3 mean decreases/increases, respectively.

Studies employing Arellano-Bond and Blundell-Bond GMM estimation for single linear dynamic panel data models are growing exponentially in number. However, for researchers it is hard to make a reasoned choice between many different possible implementations of these estimators and associated tests. By simulation the effects are examined of many options regarding: (i) reducing, extending or modifying the set of instruments; (ii) specifying the weighting matrix in relation to the type of heteroskedasticity; (iii) using (robustified) 1-step or (corrected) 2-step variance estimators; (iv) employing 1-step or 2-step residuals in Sargan-Hansen overall or incremental overidentification restrictions tests. This is all done for models in which some regressors may be either strictly exogenous, predetermined or endogenous. Surprisingly, particular asymptotically optimal and relatively robust weighting matrices are found to be superior in finite samples to ostensibly more appropriate versions. Most of the variants of tests for overidentification restrictions show serious deficiencies. A recently developed modification of GMM is found to have great potential when the cross-sectional heteroskedasticity is pronounced and the time-series dimension of the sample not too small. Finally all techniques are employed to actual data and lead to some profound insights.

We overview the main equations of the Rayleigh-Ritz variational method and discuss their connection with the problem of simultaneous diagonalization of two Hermitian matrices.

In this paper, we propose a system of nonlinear mixed variational inequality problems, which consists of two elliptic mixed variational inequality problems on Banach spaces. Under suitable assumptions, using the Kakutani-Ky Fan fixed point theorem and Minty techniques, we prove the solution set to the system of nonlinear mixed variational inequality problem is nonempty, weakly compact and unique. Additionally, we suggest a stability result for the system of nonlinear mixed variational inequality problem by perturbing the duality mappings. Furthermore, we present an optimal control problem governed by the system of nonlinear mixed variational inequality problems and establish a solvability result.

In this paper, we study a co-variational inequality problem involving Yosida approximation operators in real uniformly smooth Banach space and define an iterative method to obtain its solution. We prove some properties of Yosida approximation operator for our purpose, that is strongly accretivity and Lipschitz continuity. An existence as well as convergence result is proved for co-variational inequality problem involving Yosida approximation operators using the concept of nonexpansive sunny retraction.

We develop an action principle to construct the field equations for dissipative/resistive general relativistic two-temperature plasmas, including a neutrally charged component. The total action is a combination of four pieces: an action for a multi-fluid/plasma system with dissipation/resistivity and entrainment; the Maxwell action for the electromagnetic field; the Coulomb action with a minimal coupling of the four-potential to the charged fluxes; and the Einstein-Hilbert action for gravity (with the metric being minimally coupled to the other action pieces). We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for the neutral, positively, and negatively charged fluid species and for three associated entropy flows. The full suite of field equations is recast in the so-called ``$3 + 1$'' form (suitable for numerical simulations), where spacetime is broken up into a foliation of spacelike hypersurfaces and a prescribed ``flow-of-time''. A previously constructed phenomenological model for the resistivity is updated to include the modified heat flow and the presence of a neutrally charged species. We impose baryon number and charge conservation as well as the Second Law of Thermodynamics in order to constrain the number of free parameters in the resistivity. Finally, we take the Newtonian limit of the ``$3 + 1$'' form of the field equations which can be compared to existing non-relativistic formulations. Applications include main sequence stars, neutron star interiors, accretion disks, and the early universe.

The current paper is devoted to the introduction of simpler Eulerian variational principles from which all the relevant equations of non-barotropic stationary magnetohydrodynamics can be derived for magnetic fields which lie on surfaces. A variational principle is given in terms of three independent variables for stationary non-barotropic magnetohydrodynamic flows. This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the magnetic field, the velocity field, the specific entropy and the density. We further investigate the case in which the flow along magnetic lines is not ideal.

The current study compared the goodness of fit and estimation precision of Bayes and maximum likelihood (ML) structural equation modeling across sample sizes. Data consisted of Markov Chain Monte Carlo generated samples of 50, 75, 100, 125, 150, 200, 250, 500, 750, 1000, and 1500 observations. The Bayes and ML methods were used to estimate a structural equation model with 40 parameters, including 12 continuous observed indicators, four latent variables, and three structural paths. Analyses were conducted with the Mplus 8.0 statistical software and were replicated 500 times with each of the 22 conditions (11 sample sizes x 2 estimation methods). Indices of model fit were the Bayes information criterion, the Tucker-Lewis index, the comparative fit index, the root mean square error of approximation, the posterior predictive p-value (for Bayes models), and the ꭓ2 test (for ML models). Results showed that as the sample size increased, both estimation methods exhibited improved model fit and enhanced estimation precision, and both methods performed well with samples of 200 or larger; however, ML demonstrated a marginally superior fit with smaller samples. These findings were not consistent with previous research and suggest that ML remains a better choice with continuous data and small samples.

The general objective of the study is to analyze food insecurity determinants mainly related to food price at macro level. The study used a time series data from the year 1988 quarter one to 2018 quarter four. Our empirical finding on the macroeconomic model show the short term consequence of food price change is positive with food security (negative with food insecurity). The long term consequence of food price change is, however, negative with food security (positive with food insecurity) at macro level. From the variance decomposition, it can be learned that the speed by which the undernourished people decrease in number in the short term because of the inflation happened is higher than the speed by which the number of undernourished people increase in the long run. At macro level, concern should be made to the supply side for food security improvement.

Background: All Payer Claims Databases (APCD) are a rich source of health information, however, race and ethnicity (R&E) data are largely missing. Bayesian Improved Surname Geocoding (BISG) is a common R&E imputation method, yet, validation of BISG in APCDs is lacking. We used the BISG to impute missing R&E in the Oregon APCD. Methods: BISG imputed R&E for Asian Pacific Islanders (API), Blacks, Hispanics and Whites were contrasted to the gold standard (vital statistics) and sensitivity and specificity improvements were assessed. Logistic regression examined whether missing R&E was random across patient characteristics. Results: Among 85,857 individuals in the study, 32.1% (n=27,594) had missing R&E. Missing R&E was not randomly distributed. There were higher odds of missingness among males, Whites, those age 65 and older, and commercially insured individuals. Differences in the percent missing were also found by co-morbid conditions and mortality causes. Imputing the missing R&E with BISG method improved the sensitivity to identify White, Black, API, and Hispanics. Conclusions: APCDs can benefit from enhancing missing R&E with BISG imputation to perform more robust population-health level analyses and identify inequities according to R&E without losing power or dropping non-random records with missing R&E data.

Deep learning heavily relies on statistical correlations to drive artificial intelligence (AI) innovations, particularly in computer vision applications like autonomous driving and robotics. However, despite providing a solid foundation for deep learning, these statistical correlations can be vulnerable to unforeseen and uncontrolled factors. The lack of prior knowledge guidance can result in spurious correlations, introducing confounding factors and affecting the model's robustness. To address this challenge, recent research efforts have focused on integrating causal theory into deep learning methodologies. By modelling the inherent and unbiased causal structure, causal theory can potentially mitigate the impact of spurious correlations effectively. Hence, this paper explores the basics of causal methodologies in image classification.

What is the function of cognition? On one influential account, cognition evolved to co-ordinate behaviour with environmental change or complexity (Godfrey-Smith 1996). Liberal interpretations of this view ascribe cognition to an extraordinarily broad set of biological systems – even bacteria, which modulate their activity in response to salient external cues, would seem to qualify as cognitive agents. However, equating cognition with adaptive flexibility per se glosses over important distinctions in the way biological organisms deal with environmental complexity. Drawing on contemporary advances in theoretical biology and computational neuroscience, we cash these distinctions out in terms of different kinds of generative models, and the representational and uncertainty-resolving capacities they afford. This analysis leads us to propose a formal criterion for delineating cognition from other, more pervasive forms of adaptive plasticity. On this view, biological cognition is rooted in a particular kind of functional organisation; namely, that which enables the agent to detach from the present and engage in counterfactual (active) inference.

This paper presents a scenario evolution model for maritime accidents using Bayesian networks (BN) to predict the most likely causes of specific types of maritime incidents. The BN nodes encompass accident type, life loss contingency, accident severity, the quarter and time period of the accident, and the type and gross tonnage of the ships involved. We analyzed 5,660 global maritime accidents from 2005 to 2020. Using Netica software, we constructed a Tree Augmented Network (TAN) model, accounting for interdependencies among risk influencing factors. We validated the results through sensitivity analysis and historical accident records. Forward causal inference and reverse diagnostic inference were then performed on each node variable to investigate the accident development trend and evolution process under predetermined conditions. The findings indicate that the model can effectively predict the likelihood of various accident scenarios under specific conditions, as well as the extrapolation of accident consequences. Forward causal reasoning reveals that general cargo ships with a gross tonnage of 1-18,500 t are most likely to experience collision, grounding, and stranding accidents in the first quarter. Reverse diagnostic reasoning indicates that during early morning hours, container ships, general cargo ships, and chemical ships with a tonnage of 1-18,500 t are less likely to involve life loss in the event of collision accidents.

The adoption of Machine Learning (ML) for building emulators for complex physical processes has seen an exponential rise in the recent years. While neural networks are good function approximators, optimizing the hyper-parameters of the network to reach a global minimum is not trivial, and often needs human knowl- edge and expertise. In this light, automatic ML or autoML methods have gained large interest as they automate the process of network hyper-parameter tuning. In addition, Neural Architecture Search (NAS) has shown promising outcomes for improving model performance. While autoML methods have grown in popularity for image, text and other applications, their effectiveness for high-dimensional, complex scientific datasets remains to be investigated. In this work, a data driven emulator for turbulence closure terms in the context of Large Eddy Simulation (LES) models is trained using Artificial Neural Networks and an autoML frame- work based on Bayesian Optimization, incorporating priors to jointly optimize the hyper-parameters as well as conduct a full neural network architecture search to converge to a global minima, is proposed. Additionally, we compare the effect of using different network weight initializations and optimizers such as ADAM, SGDM and RMSProp, to explore the best performing setting. Weight and function space similarities during the optimization trajectory are investigated, and critical differences in the learning process evolution are noted and compared to theory. We observe ADAM optimizer and Glorot initialization consistently performs better, while RMSProp outperforms SGDM as the latter appears to have been stuck at a local minima. Therefore, this autoML BayesOpt framework provides a means to choose the best hyper-parameter settings for a given dataset.

Advances in remote sensing have led to use of satellite-derived rainfall products to complement the sparse rain gauge data. Although globally derived and some regional bias corrected, these products often show large discrepancies with ground measurements attributed to local and external factors that require systematic consideration. Decreasing rain gauge network however inhibits continuous validation of these products. We propose to deal with this problem by the use of Bayesian approach to merge the existing historical rain gauge information to create a consistent satellite rainfall data that can be used for climate studies. Monthly Bayesian bias correction is applied to the Climate Hazards Group Infrared Precipitation with Stations (CHIRPS v2) data to reduce systematic errors using a corresponding gridded (0.05°) rain gauge data over East Africa for a period of 33 (1981–2013) years of which 22 years are utilized to derive error fields which are then applied to an independent CHIRPS data for 11 years for validation. The bias correction is spatially and temporally assessed during the rainfall wet months of March-May (MAM), June-August (JJA) and October–December (OND) in East Africa. Results show significant reduction of systematic errors at both monthly and yearly scales and harmonization of their cumulative distributions. Monthly statistics showed a reduction of RMSD (29–56)% and MAE (28–60)% and an increase of correlations (2–32) %, while yearly ones showed reductions of RMSD (9-23)%, and MAE (7–27)% and increase of correlations (4–77)% for MAM months, reduction of RMSD (15–35)% and MAE (16–41)% and increase in correlations (5–16)% for JJA months, and reduction of RMSD (3–35)% and MAE (9–32)% and increase of correlations (3–65)% for OND months. Systematic errors of corrected data were influenced by local processes especially over Lake Victoria and high elevated areas. Large-scale circulations induced errors were mainly during JJA and OND rainfall seasons and were reduced by the separation of anomalous years during training. The proposed approach is recommended for generating long-term data for climate studies where consistencies of errors can be assumed.

In this paper we perform numerous numerical studies for the problem of low-rank matrix completion. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.

Establishing an accurate mathematical model is the foundation of simulating the motion of marine vehicles and structures, and it is the basis of modeling-based control design. System identification from observed input-output data is a practical and powerful method. However, for modeling objects with different characteristics and known information, a single modeling framework can hardly meet the requirements of model establishment. Moreover, there are some challenges in system identification, such as parameter drift and overfitting. In this work, three robust methods are proposed for generating ocean hydrodynamic models based on Bayesian regression. Two Bayesian techniques, semi-conjugate linear regression and noisy input Gaussian process regression, are used for parametric and nonparametric gray-box modeling and black-box modeling. The experimental free-running tests of the KVLCC2 ship model and a multi-freedom wave energy converter (WEC) are used to validate the proposed Bayesian models. The results demonstrate that the proposed schemes for system identification of the ship and WEC have good generalization ability and robustness. Finally, the developed modeling methods are evaluated considering the aspects required conditions, operating characteristics and prediction accuracy.

We compare the well known Rayleigh-Ritz variational method (RRVM) with a recently proposed approach based on supersymmetric quantum mechanics and the Gram-Schmidt orthogonalization method (SSQMGS). We apply both procedures to a particular class of double-well harmonic oscillators that had been conveniently chosen for the application of the latter approach. The RRVM eigenvalues converge smoothly from above providing much more accurate results with less computational effort. Present results show that the unproved SSQMGS upper bounds do not hold.

In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra’s integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.