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Diversity is crucial for metaheuristic algorithms. It prevents early convergence, balances exploration and exploitation, and helps to avoid local optima. Traditional metaheuristic algorithms tend to rely on a single strategy for generating new solutions, often resulting in a lack of diversity. In contrast, employing multiple strategies encourages a variety of search behaviors and a diverse pool of potential solutions, thereby improving the exploration of the search space. Evolutionary Game Theory (EGT) modifies agents' strategies through competition, promoting successful strategies and eliminating weaker ones. Structured populations, as opposed to unstructured ones, preserve diverse strategies through localized competition, meaning that an individual's strategy is influenced by only a subset or group of the population and not all elements. This paper presents a novel metaheuristic method based on EGT applied to structured populations. Initially, individuals are positioned near optimal regions using the Metropolis–Hastings algorithm. Subsequently, each individual is endowed with a unique search strategy. Considering a certain number of clusters, the complete population is segmented. Within these clusters, the method enhances search efficiency and solution quality by adapting all strategies through an intra-cluster competition. To assess the effectiveness of the proposed method, it has been compared against several well-known metaheuristic algorithms across a suite of 30 test functions. The results indicated that the new methodology outperformed the established techniques, delivering higher-quality solutions and faster convergence rates. [ABSTRACT FROM AUTHOR]

We adapt the Metropolis–Hastings (MH) algorithm to facilitate construction of the ensemble solution of the nonlinear implicit inverse problem. The solution variable is the aggregation of the parameters of interest (model parameters) and the data. The prior probability density function (pdf) is the possibly-non-Normal joint pdf of the prior model parameters and the noisy data, and is defined in a high-dimensional space. The posterior pdf of the solution (estimated model parameter and predicted data) is the prior pdf evaluated on the lower-dimensional manifold defined by the theory. We adapt the MH algorithm to ensure that successors always satisfy the theory (that is, are on the manifold) and provide a rule for computing the probability of a given successor. Key parts of this adaption are the use of singular value decomposition to identify subspaces tangent to the manifold, and orthogonal projection, to move a preliminary estimate of a successor onto the manifold. We apply the adapted methodology to three exemplary problems: fitting a straight line to (x,y) data, when both x and y have measurement noise; fitting a circle to noisy (x,y) data, and finding a filter that takes one noisy time series into another. In these cases, the scatter of the ensemble solution about the linearized maximum likelihood solution is roughly consistent with the linearized posterior covariance, but with some non-Normal behavior. We demonstrate the usefulness of the ensemble solutions by computing empirical pdfs of several informative statistical parameters, the calculation of which would be difficult by traditional means. [ABSTRACT FROM AUTHOR]

In this article, the video game Dota 2 is used as an illustration of video games where two teams have to confront. This is a very popular game where billions of matches are available for enhancing statistical analysis and fostering further method developments. Here, we focus on sampling teams or pairs of teams favouring more imbalanced matches, based upon the scores observed either for one team or for a couple of teams. An artificial neural network models the expected outcome which is then used to sample teams through a Metropolis-Hastings algorithm. The main result is establishing the polynomial convergence speed bound for both cases, that is sampling random teams and sampling random pairs of teams. An empirical experiment is also provided when sampling pairs of teams for Dota after learning matches outcomes from a database of 2 million matches, showing that the convergence may happen much more quickly. [ABSTRACT FROM AUTHOR]

Simple Summary: Chimeric antigen receptor (CAR)-T cell therapy is a promising treatment for highly resistant blood cancers, using genetically modified T cells from the patient or a donor. While CAR-T therapy has been successful in pre-clinical and clinical stages for cancer treatment, it also presents challenges, including cytokine release syndrome. To improve the efficacy and reduce side effects, there is a need to better understand CAR-T cell behavior. We aimed to develop a mathematical framework that describes CAR-T behavior using ordinary differential equations (ODEs) and Bayesian parameter estimation (using advanced algorithms including Metropolis–Hastings, DEMetropolis, and DEMetropolisZ). This model will help to understand CAR-T behavior and, by extension, help to improve the effectiveness and efficacy of therapy in a clinical setting. Chimeric antigen receptor (CAR)-T cell therapy represents a breakthrough in treating resistant hematologic cancers. It is based on genetically modifying T cells transferred from the patient or a donor. Although its implementation has increased over the last few years, CAR-T has many challenges to be addressed, for instance, the associated severe toxicities, such as cytokine release syndrome. To model CAR-T cell dynamics, focusing on their proliferation and cytotoxic activity, we developed a mathematical framework using ordinary differential equations (ODEs) with Bayesian parameter estimation. Bayesian statistics were used to estimate model parameters through Monte Carlo integration, Bayesian inference, and Markov chain Monte Carlo (MCMC) methods. This paper explores MCMC methods, including the Metropolis–Hastings algorithm and DEMetropolis and DEMetropolisZ algorithms, which integrate differential evolution to enhance convergence rates. The theoretical findings and algorithms were validated using Python and Jupyter Notebooks. A real medical dataset of CAR-T cell therapy was analyzed, employing optimization algorithms to fit the mathematical model to the data, with the PyMC library facilitating Bayesian analysis. The results demonstrated that our model accurately captured the key dynamics of CAR-T cell therapy. This conclusion underscores the potential of parameter estimation to improve the understanding and effectiveness of CAR-T cell therapy in clinical settings. [ABSTRACT FROM AUTHOR]

Given a target probability density known up to a normalizing constant, the Metropolis–Hastings algorithm simulates realizations from a Markov chain which are eventual realizations from the target probability density. A key element for ensuring a reliable Metropolis–Hastings simulation experiment is understanding how quickly the simulation will generate a representative sample from target density. This corresponds to understanding the convergence properties of the Metropolis–Hastings Markov chain. State‐of‐the‐art methods for convergence analysis of Metropolis–Hastings algorithms are considered and reviewed. Practically important topics are discussed for an interdisciplinary audience. This includes convergence properties in high dimensions, proper tuning, initialization, and limitations of current convergence analyses. This article is categorized under:Statistical and Graphical Methods of Data Analysis > Markov Chain Monte CarloStatistical and Graphical Methods of Data Analysis > Monte Carlo MethodsStatistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory [ABSTRACT FROM AUTHOR]

This paper focuses on the mixture Gamma distribution and uses the maximum likelihood and Bayesian techniques to estimate its parameters. This study uses Expectation Maximization Algorithm (EM) to find the maximum likelihood estimators and the random Metropolis-Hastings algorithm is used to simulate the Bayesian estimates of the parameters of mixture gamma distribution. then these estimates are compared by using the sum of the modulus of the bias (MBias), and the root-mean square error (RMSE). It has been shown that the Bayesian estimator is better than the maximum likelihood estimator.

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost‐effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation‐Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS‐based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older. [ABSTRACT FROM AUTHOR]

In this paper, we propose new Metropolis–Hastings and simulated annealing algorithms on a finite state space via modifying the energy landscape. The core idea of landscape modification rests on introducing a parameter c , such that the landscape is modified once the algorithm is above this threshold parameter to encourage exploration, while the original landscape is utilized when the algorithm is below the threshold for exploitation purposes. We illustrate the power and benefits of landscape modification by investigating its effect on the classical Curie–Weiss model with Glauber dynamics and external magnetic field in the subcritical regime. This leads to a landscape-modified mean-field equation, and with appropriate choice of c the free energy landscape can be transformed from a double-well into a single-well landscape, while the location of the global minimum is preserved on the modified landscape. Consequently, running algorithms on the modified landscape can improve the convergence to the ground state in the Curie–Weiss model. In the setting of simulated annealing, we demonstrate that landscape modification can yield improved or even subexponential mean tunnelling time between global minima in the low-temperature regime by appropriate choice of c , and we give a convergence guarantee using an improved logarithmic cooling schedule with reduced critical height. We also discuss connections between landscape modification and other acceleration techniques, such as Catoni's energy transformation algorithm, preconditioning, importance sampling, and quantum annealing. The technique developed in this paper is not limited to simulated annealing, but is broadly applicable to any difference-based discrete optimization algorithm by a change of landscape. [ABSTRACT FROM AUTHOR]

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration. [ABSTRACT FROM AUTHOR]

Deep generative models (DGM) are increasingly employed in emergent communication systems. However, their application in multimodal data contexts is limited. This study proposes a novel model that combines multimodal DGM with the Metropolis-Hastings (MH) naming game, enabling two agents to focus jointly on a shared subject and develop common vocabularies. The model proves that it can handle multimodal data, even in cases of missing modalities. Integrating the MH naming game with multimodal variational autoencoders (VAE) allows agents to form perceptual categories and exchange signs within multimodal contexts. Moreover, fine-tuning the weight ratio to favor a modality that the model could learn and categorize more readily improved communication. Our evaluation of three multimodal approaches - mixture-of-experts (MoE), product-of-experts (PoE), and mixture-of-product-of-experts (MoPoE)-suggests an impact on the creation of latent spaces, the internal representations of agents. Our results from experiments with the MNIST + SVHN and Multimodal165 datasets indicate that combining the Gaussian mixture model (GMM), PoE multimodal VAE, and MH naming game substantially improved information sharing, knowledge formation, and data reconstruction. [ABSTRACT FROM AUTHOR]

We provide a comparison between marginal likelihood and data augmented Markov chain Monte Carlo (MCMC) algorithms for Bayesian estimation of hidden Markov models. In particular, we focus on a specification of these models based on a multivariate Gaussian distribution for the response variables. We evaluate the performance of both methods on the basis of simulated samples and an empirical application, where we compare these approaches in terms of standard measures of estimation and time efficiency. The results show that the augmented algorithm is preferable, obtaining optimal convergence properties and producing larger values of the effective sample size. Instead of using variable dimensional techniques for model selection, we suggest a method based on the so-called parallel sampling for this aim. [ABSTRACT FROM AUTHOR]

The noterate is a tool for predicting home mortgage rates, it is often skewed and has missing information. The noterate could be affected by incomplete or inaccurate data, thus leading to inaccurate predictions. Financial organizations including mortgage companies or banks need to consider the risk of uncertainty carefully and make a more accurate prediction based on some suitable models. To deal with this situation, in this paper we compared six computational statistical methods, including the ordinary least square model, maximum likelihood estimation, maximum a posterior, bootstrapping, Metropolis-Hastings, and Gibbs sampling method on a mortgage dataset. Based on the k fold cross-validation technique and four metrics including mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and mean absolute percentage error (MAPE), the bootstrapping method outperforms other methods. In practice, this method is recommended for predicting noterate. [ABSTRACT FROM AUTHOR]

Under mild assumptions, we show that the exact convergence rate in total variation is also exact in weaker Wasserstein distances for the Metropolis–Hastings independence sampler. We develop a new upper and lower bound on the worst-case Wasserstein distance when initialized from points. For an arbitrary point initialization, we show that the convergence rate is the same and matches the convergence rate in total variation. We derive exact convergence expressions for more general Wasserstein distances when initialization is at a specific point. Using optimization, we construct a novel centered independent proposal to develop exact convergence rates in Bayesian quantile regression and many generalized linear model settings. We show that the exact convergence rate can be upper bounded in Bayesian binary response regression (e.g. logistic and probit) when the sample size and dimension grow together. [ABSTRACT FROM AUTHOR]

Deep generative models (DGM) are increasingly employed in emergent communication systems. However, their application in multimodal data contexts is limited. This study proposes a novel model that combines multimodal DGM with the Metropolis-Hastings (MH) naming game, enabling two agents to focus jointly on a shared subject and develop common vocabularies. The model proves that it can handle multimodal data, even in cases of missing modalities. Integrating the MH naming game with multimodal variational autoencoders (VAE) allows agents to form perceptual categories and exchange signs within multimodal contexts. Moreover, fine-tuning the weight ratio to favor a modality that the model could learn and categorize more readily improved communication. Our evaluation of three multimodal approaches -- mixture-of-experts (MoE), product-of-experts (PoE), and mixture-of-product- of-experts (MoPoE)-suggests an impact on the creation of latent spaces, the internal representations of agents. Our results from experiments with the MNIST + SVHN and Multimodal165 datasets indicate that combining the Gaussian mixture model (GMM), PoE multimodal VAE, and MH naming game substantially improved information sharing, knowledge formation, and data reconstruction. [ABSTRACT FROM AUTHOR]

For statistical inference of competing risks under type-II progressive censoring, lifetimes are modeled by an inverted exponential Rayleigh distribution, which allows the use of a non-monotonic hazard function. Maximum-likelihood estimators for all parameters exist and are unique. The Newton-Raphson algorithm and maximum stochastic expectation each provide estimates. Confidence intervals result from the Fisher matrix and the asymptotic normality of maximum-likelihood estimators. For small samples, the Bootstrap estimators of the parameters do not need to be asymptotically normal. In addition, the Monte Carlo method with the Metropolis-Hastings algorithm and importance sampling allow for Bayesian estimation, with the associated highest posterior-density intervals. The Bayesian method takes account of prior information, contrary to the frequentist method. The Bootstrap method improves the precision of the estimation, especially in the case of small sample sizes. The estimated range obtained by Bootstrap is between 20% and 60% smaller than that obtained by maximum likelihood. Frequentist and Bayesian estimations using the inverted exponentiated Rayleigh distribution under type-II progressive censoring allow for fitting empirical mouse mortality data and obtaining parameter estimates of this distribution. A quantile-dependent criterion and a quantile-independent criterion are used to determine the optimal censoring and to design the experiment. [ABSTRACT FROM AUTHOR]

Multilevel modeling is a modern approach to deal with hierarchical or a nested data structure which can assess the variability between clusters. Bayesian Markov Chain Monte Carlo (MCMC) methods of estimations are advanced methods applicable for estimating multilevel models. However, these estimation methods are not as yet tested to identify its' performances as well as the properties associated with these estimation methods. This study targets to conduct a comparison of Bayesian MCMC methods which are developed for multilevel models where the response is normally distributed. The comparison is based upon extensive simulations and an application to a real-life dataset. The performance of Gibbs sampling (GS) and Metropolis Hastings (MH) methods are compared using a simulation study and additionally the factors which can affect the performance of both MCMC methods are identified. Practicality of these methods in real world scenario is confirmed through the application of MCMC method to a dataset. In the simulations though the Metropolis Hastings (MH) shows slightly better performance than Gibbs, there is no evidence to indicate that significant differences exist between these methods except for small samples where MH is superior. The results from the example are not as clear as from the simulations. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to present a Bayesian analysis of Multivariate GARCH(l, m) (M-GARCH) models including estimation of the coefficient parameters as well as the model order, by combining a set of existing MCMC algorithms in the literature. The proposed algorithm focuses on the BEKK formulation of the multivariate GARCH model. The estimation procedure will be designed as a custom MCMC with embedded Reversible Jump MCMC (RJMCMC) and Delayed Rejection Metropolis-Hastings (DRMH) steps implemented using the statistical software R. The RJMCMC steps allow three variants of BEKK models (constant, diagonal and full) to be indexed and this index included as a parameter to be estimated. The proposed MCMC algorithms are validated using extensive simulation experiments followed by a case study using bivariate data derived from the daily share prices for BHP Group Limited, Rio Tinto Group, and Fortescue Metals Group Limited on the ASX over from September 2013 to December 2021. [ABSTRACT FROM AUTHOR]

Nowadays, online users write short messages to share their feelings on social networking sites, such as discussion forums, question answering websites, etc., making these sites very popular. The increase in these short-term messages causes a huge data sparsity, making emotion recognition a challenging task. Therefore, a word co-occurrence pattern called biterms is generated from a large-scale dataset to prevent severe data sparsity issues. The topic modeling algorithms and acceleration algorithms are implemented to extract more reliable topics from the group of terms. Based on biterm technique, in this paper, a new algorithm called "Affected biterm emotion topic" is proposed for emotion recognition from a short text. For the experimental purpose, two popular short text datasets, SemEval and International Survey on Emotion Antecedents and Reactions (ISEAR), are used to investigate the performance of the proposed algorithm with the benchmark methods light latent dirichlet allocation (LLDA), biterm topic model (BTM), emotion-topic model (ETM), contextual sentiment topic model (CSTM), Sentiment latent topic model (SLTM) and siasme network based supervised topic model (SNSTM). The proposed algorithm is evaluated using the benchmark methods for mean, variance, and accuracy. The experimental result shows that the proposed algorithm is effective in analyzing emotions. [ABSTRACT FROM AUTHOR]

Millions of people died in the COVID-19 pandemic, which pressured hospitals and healthcare workers into keeping up with the speed and intensity of the outbreak, resulting in a scarcity of ICU beds for COVID-19 patients. Therefore, researchers have developed machine learning (ML) algorithms to assist in identifying patients at increased risk of requiring an ICU bed. However, many of these studies used state-of-the-art ML algorithms with arbitrary or default hyperparameters to control the learning process. Hyperparameter optimization is essential in enhancing the classification effectiveness and ensuring the optimal use of ML algorithms. Therefore, this study utilized an improved Hunger Games Search Optimization (HGSO) algorithm coupled with a robust extreme gradient boosting (XGB) classifier to predict a COVID-19 patient's need for ICU transfer. To further mitigate the random initialization inherent in HGSO and facilitate an efficient convergence toward optimal solutions, the Metropolis–Hastings (MH) method is proposed for integration with HGSO. In addition, population diversity was reintroduced to effectively escape local optima. To evaluate the efficacy of the MH-based HGSO algorithm, the proposed method was compared with the original HGSO algorithm using the Congress on Evolutionary Computation benchmark function. The analysis revealed that the proposed algorithm converges better than the original method and exhibits statistical significance. Consequently, the proposed algorithm optimizes the XGB hyperparameters to further predict the need for ICU transfer for COVID-19 patients. Various evaluation metrics, including the receiver operating curve (ROC), precision–recall curve, bootstrap ROC, and recall vs. decision boundary, were used to estimate the effectiveness of the proposed HGSOXGB model. The model achieves the highest accuracy of 97.39% and an area under the ROC curve of 99.10% compared with other classifiers. Additionally, the important features that significantly affect the prediction of ICU transfer need using XGB were calculated. [ABSTRACT FROM AUTHOR]

In this article, we consider the preconditioned Hamiltonian Monte Carlo (pHMC) algorithm defined directly on an infinite-dimensional Hilbert space. In this context, and under a condition reminiscent of strong log-concavity of the target measure, we prove convergence bounds for adjusted pHMC in the standard 1-Wasserstein distance. The arguments rely on a synchronous coupling of two copies of pHMC, which is controlled by adapting elements from Bou-Rabee, Eberle and Zimmer (2020). [ABSTRACT FROM AUTHOR]

Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis‐Hastings warm‐starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis‐Hastings warm‐starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1‐depth QAOA. [ABSTRACT FROM AUTHOR]

Markov Chain Monte Carlo (MCMC) approaches are widely used for tuning model parameters to fit process measurements. While modern probabilistic programming languages (PPLs) such as Stan, PyMC, and Turing have made it easier to implement efficient MCMC samplers, configuring them for high dimensional and multi-modal parameter distributions remains a challenging task. In Pandey and Lie (2022), the No-U-Turn Sampler (NUTS) was employed via Turing to estimate parameters of an air-cooled synchronous generator model using real-world experimental data, but the produced posterior distributions were excessively narrow. The present study extends the findings in Pandey and Lie (2022) by producing more realistic parameter estimates using the same data. To accomplish this, the study first reviews the basics of MCMC; it offers some general advice for choosing appropriate settings for MCMC to ensure successful estimation, as well a discussion of the impact of measurement data on the computation of posteriors. The study then implements the simple classical MCMC technique, Metropolis, from scratch to estimate the generator model parameters, providing more insight into MCMC — its fundamental process and terminology. Finally, the knowledge gained is applied to select appropriate settings for NUTS — implemented via Turing — that yield more accurate parameter estimates.

Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient sampling from the posterior distribution of parameters, and standard algorithms, such as random walk Metropolis-Hastings or Hamiltonian Monte Carlo algorithms, are typically used. Herein, we developed an efficient Metropolis-Hastings algorithm and importance sampler to simulate from the posterior distribution of the parameters of Poisson log-linear models under conditional Gaussian priors with superior performance with respect to the state-of-the-art alternatives. The key for both algorithms is the introduction of a proposal density based on a Gaussian approximation of the posterior distribution of parameters. Specifically, our result leverages the negative binomial approximation of the Poisson likelihood and the successful Pólya-gamma data augmentation scheme. Via simulation, we obtained that the time per independent sample of the proposed samplers is competitive with that obtained using the successful Hamiltonian Monte Carlo sampling, with the Metropolis-Hastings showing superior performance in all scenarios considered. for this article are available online. [ABSTRACT FROM AUTHOR]

We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis--Hastings method. Our resulting algorithm is able to sample from a specified measure on partitions or spanning forests. Being able to sample from a specified measure is a requirement of what we consider as the gold standard in quantifying the extent to which a particular map is a gerrymander. Our proposal chain modifies the recently developed method called recombination (ReCom), which draws spanning trees on joined partitions and then randomly cuts them to repartition. We improve the computational efficiency by augmenting the statespace from partitions to spanning forests. The extra information accelerates the computation of the forward and backward proposal probabilities which are required for the Metropolis--Hastings algorithm. We demonstrate this method by sampling redistricting plans on several measures of interest and find promising convergence results on several key observables of interest. We also explore some limitations in the measures that are efficient to sample from and investigate the feasibility of using parallel tempering to extend this space of measures. [ABSTRACT FROM AUTHOR]

Generalized progressively Type-II hybrid strategy has been suggested to save both the duration and cost of a life test when the experimenter aims to score a fixed number of failed units. In this paper, using this mechanism, the maximum likelihood and Bayes inferential problems for unknown model parameters, in addition to both reliability, and hazard functions of the inverted exponentiated Rayleigh model, are acquired. Applying the observed Fisher data and delta method, the normality characteristic of the classical estimates is taken into account to derive confidence intervals for unknown parameters and several indice functions. In Bayes' viewpoint, through independent gamma priors against both symmetrical and asymmetrical loss functions, the Bayes estimators of the unknown quantities are developed. Because the Bayes estimators are acquired in complicated forms, a hybrid Monte-Carlo Markov-chain technique is offered to carry out the Bayes estimates as well as to create the related highest posterior density interval estimates. The precise behavior of the suggested estimation approaches is assessed using wide Monte Carlo simulation experiments. Two actual applications based on actual data sets from the mechanical and chemical domains are examined to show how the offered methodologies may be used in real current events. [ABSTRACT FROM AUTHOR]

Trees are common natural objects widely distributed in urban areas. The modeling quality of trees has significant visual effects for urban modeling. Tree models directly from the oblique photogrammetry pipeline are erratic because tree textures are repeating and confusing. Existing tree modeling approaches either cannot deal with the input data of poor quality or are time-consuming. This paper presents an oblique photogrammetry-supporting procedural tree modeling approach to solve this problem. Specifically, we propose a point cloud data-supported hybrid parametric model that models trees by simulating the growth of natural trees. To solve the challenging optimization problem in high dimensional space defined by the parametric model, a Control Parameter Analysis (CPA)-based optimization method is proposed to find the approximate solution with the highest resemblance to the input data. Finally, an automatic level of detail (LOD) control method of tree models is proposed to form a complete workflow for rendering the urban scenes. Experimental results indicate that the proposed method can generate procedural tree models in urban areas with satisfying accuracy and efficiency. The mean normalized distance between the generated tree models and input data in the test regions is 0.022, and it takes about ten minutes to generate each tree model. Our code is available at https://github.com/lelleMU/Procedrual_Tree_Modeling. [ABSTRACT FROM AUTHOR]

The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis–Hastings (MH) algorithms. Recently, acceptance probabilities other than MH are being employed in problems with intractable target distributions. There are few resources available on tuning the Gaussian proposal distributions for this situation. We obtain optimal scaling results for a general class of acceptance functions, which includes Barker's and lazy MH. In particular, optimal values for Barker's algorithm are derived and found to be significantly different from that obtained for the MH algorithm. Our theoretical conclusions are supported by numerical simulations indicating that when the optimal proposal variance is unknown, tuning to the optimal acceptance probability remains an effective strategy. [ABSTRACT FROM AUTHOR]

The state-space model is a powerful statistical tool to estimate linear or non-linear discrete-time dynamic systems. This model naturally leads to the estimation problem of the time-varying parameters of the discovery-time demographic version of the susceptible-infected-recovered (SIR) model that we consider. In this paper, we consider computational methods to perform Bayesian inference on state-space models for analysing time-series data. We compare the three popular Bayesian computational methods for state-space models: the adaptive Metropolis-within-Gibbs algorithm, Liu and West's algorithm and variational approximation method based on Gaussian distributions. The performances of the three methods are compared based on synthetic datasets. Furthermore, we analyse the trend of the spread of COVID-19 in South Korea to point out the limitations of existing methods and derive meaningful results. [ABSTRACT FROM AUTHOR]

We propose a sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature – the adaptive Metropolis sampler and the two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly very useful for high-dimensional posterior sampling in Bayesian models with expensive likelihoods. In the first stage of the proposed algorithm, an adaptive proposal is used based on the previously sampled states and the corresponding acceptance probability is computed based on an approximated inexpensive target density. The true expensive target density is evaluated while computing the second stage acceptance probability only if the proposal is accepted in the first stage. The adaptive nature of the algorithm guarantees faster convergence of the chain and very good mixing properties. On the other hand, the two-stage approach helps in rejecting the bad proposals in the inexpensive first stage, making the algorithm computationally efficient. As the proposals are dependent on the previous states the chain loses its Markov property, but we prove that it retains the desired ergodicity property. The performance of the proposed algorithm is compared with the existing algorithms in two simulated and two real data examples. [ABSTRACT FROM AUTHOR]

We establish conditions under which Metropolis-Hastings (MH) algorithms with a position-dependent proposal covariance matrix will or will not have the geometric rate of convergence. Some of the diffusions based MH algorithms like the Metropolis adjusted Langevin algorithm (MALA) and the pre-conditioned MALA (PCMALA) have a position-independent proposal variance. Whereas, for other modern variants of MALA like the manifold MALA (MMALA) that adapt to the geometry of the target distributions, the proposal covariance matrix changes in every iteration. Thus, we provide conditions for geometric ergodicity of different variations of the Langevin algorithms. These results have important practical implications as these provide crucial justification for the use of asymptotically valid Monte Carlo standard errors for Markov chain based estimates. The general conditions are verified in the context of conditional simulation from the two most popular generalized linear mixed models (GLMMs), namely the binomial GLMM with the logit link and the Poisson GLMM with the log link. Empirical comparison in the framework of some spatial GLMMs shows that the computationally less expensive PCMALA with an appropriately chosen pre-conditioning matrix may outperform the MMALA. [ABSTRACT FROM AUTHOR]

The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model's parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom. [ABSTRACT FROM AUTHOR]

This study introduces a unique flexible family of discrete probability distributions for modeling extreme count and zero-inflated count data with different failure rates. Certain significant mathematical properties, such as the cumulant generating function, moment generating function, dispersion index, L-moments, ordinary moments, and central moment are derived. The new failure rate function offers a wide range of flexibility, including "upside down", "monotonically decreasing", "bathtub", "monotonically increasing" and "decreasing-constant failure rate" and "constant". Moreover, the new probability mass function accommodates many useful shapes including the "right skewed function with no peak", "symmetric", "right skewed with one peak" and "left skewed with one peak". To obtain significant characterization findings, the hazard function and the conditional expectation of certain function of the random variable are both employed. Both Bayesian and non-Bayesian estimate methodologies are considered when estimating, assessing, and comparing inferential efficacy. The Bayesian estimation approach for the squared error loss function is suggested, and it is explained. Markov chain Monte Carlo simulation studies are performed using the Metropolis Hastings algorithm and the Gibbs sampler to compare non-Bayesian vs. Bayesian results. Four real-world applications of count data sets are used to evaluate the Bayesian versus non-Bayesian techniques. Four more real count data applications are used to illustrate the significance and versatility of the new discrete class. [ABSTRACT FROM AUTHOR]

In this paper, a progressive type-II censoring strategy is used to estimate the parameters, reliability and hazard rate functions of the exponentiated moment exponential distribution. The maximum likelihood and Bayesian techniques have been used to estimate the proposed estimators. Gamma (informative) and uniform (non-informative) priors are taken into account under the squared error loss function to produce the Bayesian estimators. The highest posterior density interval estimations and the 95% approximate confidence intervals along with coverage probability are calculated. In order to evaluate the effectiveness of estimates produced by the Metropolis-Hastings sampling algorithms, we provide a numerical research. According to the study's findings, the Bayes estimates under informative priors are typically more accurate than other estimates. [ABSTRACT FROM AUTHOR]

The lifetime performance index plays a crucial role in manufacturing procedures as it provides valuable insights into the overall quality of a product. Considering the Gompertz distribution as a widely applicable statistical distribution, this index to emphasize the effect in analyzing lifetime data. This paper investigates the inference techniques associated with the lifetime performance index for the Gompertz distribution when k -record values are available. For this problem, two innovative methods are introduced utilizing the concept of the generalized pivotal variable. These methods are not only applicable to hypothesis tests but also enable the construction of confidence intervals. To further enhance the accuracy of estimation, the study proposes Bayesian estimation techniques based on the Metropolis–Hastings algorithms. To assess the efficacy of these methods, a simulation study is conducted. The results demonstrate that all three procedures exhibit exceptional performance, even when confronted with datasets consisting of small k -record values. Moreover, a dataset is utilized to demonstrate the implementation of these three methods. [ABSTRACT FROM AUTHOR]

Models for count data which are temporally correlated have been studied using many conditional distributions, such as the Poisson distribution, and the insertion of different dependence structures. Nonetheless, excess of zeros and over dispersion may be observed during the counting process and need to be considered when modelling and choosing a conditional distribution. In this paper, we propose models for counting time series using zero-adjusted distributions by inserting a dependence structure following the ARMA(p, q) process on a Bayesian framework. We perform a simulation study using the proposed Bayesian analysis and analyse the monthly time series of the number of deaths due to dengue haemorrhagic fever (ICD-A91) in Brazil.

Utilizing degraded quality waters such as saline water as irrigation water with proper management methods such as leaching application is a potential answer to water scarcity in agricultural systems. Leaching application requires understanding the relationship between the amount of irrigation water and its quality with the dynamic of salts in the soil. The HYDRUS-1D model can simulate the dynamic of soil salinity under saline water irrigation conditions. However, these simulations are subject to uncertainty. A study was conducted to assess the uncertainty of the HYDRUS-1D model parameters and outputs to simulate the dynamic of salts under saline water irrigation conditions using the Markov Chain Monte Carlo (MCMC) based Metropolis-Hastings algorithm in the R-Studio environment. Results indicated a low level of uncertainty in parameters related to the advection term (water movement simulation) and water stress reduction function for root water uptake in the solute transport process. However, a higher level of uncertainty was detected for dispersivity and diffusivity parameters, possibly because of the study's scale or some error in initial or boundary conditions. The model output (predictive) uncertainty showed a high uncertainty in dry periods compared to wet periods (under irrigation or rainfall). The uncertainty in model parameters was the primary source of total uncertainty in model predictions. The implementation of the Metropolis-Hastings algorithm for the HYDRUS-1D was able to conveniently estimate the residual water content (θr) value for the water simulation processes. The model's performance in simulating soil water content and soil water electrical conductivity (ECsw) was good when tested with the 50% quantile of the posterior distribution of the parameters. Uncertainty assessment in this study revealed the effectiveness of the Metropolis-Hastings algorithm in exploring uncertainty aspects of the HYDRUS-1D model for reproducing soil salinity dynamics under saline water irrigation at a field scale. [ABSTRACT FROM AUTHOR]

A general framework is introduced to estimate how much external information has been infused into a search algorithm, the so-called active information. This is rephrased as a test of fine-tuning, where tuning corresponds to the amount of pre-specified knowledge that the algorithm makes use of in order to reach a certain target. A function f quantifies specificity for each possible outcome x of a search, so that the target of the algorithm is a set of highly specified states, whereas fine-tuning occurs if it is much more likely for the algorithm to reach the target as intended than by chance. The distribution of a random outcome X of the algorithm involves a parameter θ that quantifies how much background information has been infused. A simple choice of this parameter is to use θ f in order to exponentially tilt the distribution of the outcome of the search algorithm under the null distribution of no tuning, so that an exponential family of distributions is obtained. Such algorithms are obtained by iterating a Metropolis–Hastings type of Markov chain, which makes it possible to compute their active information under the equilibrium and non-equilibrium of the Markov chain, with or without stopping when the targeted set of fine-tuned states has been reached. Other choices of tuning parameters θ are discussed as well. Nonparametric and parametric estimators of active information and tests of fine-tuning are developed when repeated and independent outcomes of the algorithm are available. The theory is illustrated with examples from cosmology, student learning, reinforcement learning, a Moran type model of population genetics, and evolutionary programming. [ABSTRACT FROM AUTHOR]

A delayed-acceptance version of a Metropolis–Hastings algorithm can be useful for Bayesian inference when it is computationally expensive to calculate the true posterior, but a computationally cheap approximation is available; the delayed-acceptance kernel targets the same posterior as its associated "parent" Metropolis-Hastings kernel. Although the asymptotic variance of the ergodic average of any functional of the delayed-acceptance chain cannot be less than that obtained using its parent, the average computational time per iteration can be much smaller and so for a given computational budget the delayed-acceptance kernel can be more efficient. When the asymptotic variance of the ergodic averages of all L 2 functionals of the chain are finite, the kernel is said to be variance bounding. It has recently been noted that a delayed-acceptance kernel need not be variance bounding even when its parent is. We provide sufficient conditions for inheritance: for non-local algorithms, such as the independence sampler, the discrepancy between the log density of the approximation and that of the truth should be bounded; for local algorithms, two alternative sets of conditions are provided. As a by-product of our initial, general result we also supply sufficient conditions on any pair of proposals such that, for any shared target distribution, if a Metropolis-Hastings kernel using one of the proposals is variance bounding then so is the Metropolis-Hastings kernel using the other proposal. [ABSTRACT FROM AUTHOR]

In positron emission tomography (PET) and X-ray computed tomography (CT), reducing radiation dose can cause significant degradation in image quality. For image quality enhancement in low-dose PET and CT, we propose a novel theoretical adversarial and variational deep neural network (DNN) framework relying on expectation maximization (EM) based learning, termed adversarial EM (AdvEM). AdvEM proposes an encoder–decoder architecture with a multiscale latent space, and generalized-Gaussian models enabling datum-specific robust statistical modeling in latent space and image space. The model robustness is further enhanced by including adversarial learning in the training protocol. Unlike typical variational-DNN learning, AdvEM proposes latent-space sampling from the posterior distribution, and uses a Metropolis–Hastings scheme. Unlike existing schemes for PET or CT image enhancement which train using pairs of low-dose images with their corresponding normal-dose versions, we propose a semi-supervised AdvEM (ssAdvEM) framework that enables learning using a small number of normal-dose images. AdvEM and ssAdvEM enable per-pixel uncertainty estimates for their outputs. Empirical analyses on real-world PET and CT data involving many baselines, out-of-distribution data, and ablation studies show the benefits of the proposed framework. [Display omitted] • Expectation-maximization based variational deep learning for Low-Dose PET and CT • Adversarial learning for improved robustness with respect to out-of-distribution data • Variational learning with posterior distribution sampling using Metropolis Hastings • Multiscale latent space modeled by a Generalized Gaussian distribution • Semi-supervised learning utilizing a larger set of low-dose images than normal-dose • The framework supports uncertainty mapping corresponding to the outputs it produces [ABSTRACT FROM AUTHOR]

Multi‐state models are frequently applied to represent processes evolving through a discrete set of states. Important classes of multi‐state models arise when transitions between states may depend on the time passed since entry into the current state or on the time elapsed from the start of the process. The former models are called semi‐Markov while the latter are known as inhomogeneous Markov models. Inference for both the models presents computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. In fact, in both the cases, the likelihood function is not available in closed form. To obtain Bayesian inference under these two classes of models, we reconstruct the entire unobserved trajectories conditioned on the observed points via a Metropolis‐Hastings algorithm. As proposal density we use that given by the nested Markov models whose conditioned trajectories can easily be drawn with the uniformization technique. The resulting inference is illustrated via simulation studies and the analysis of two benchmark datasets for multi‐state models. [ABSTRACT FROM AUTHOR]

Since the introduction of African swine fever (ASF) to Georgia in 2007, the disease has spread to many other countries including South Korea. Initial detection of ASF from wild boars (WB) in South Korea was reported in early October 2019. Since then, more than a thousand WB samples collected from the northern part of the country have been confirmed as ASF positive (2.9% of ASF positivity among WB samples collected until June 2020), indicating that the disease is endemic in the WB populations. To control the disease, multiple layers of fence‐lines have been erected. Nevertheless, outbreaks continuously occurred across the fence, requiring a better understanding of the spatial transmission mechanism of ASF in WBs. Hence, we developed a novel ASF transmission model to estimate ecological and epidemiological parameters related to the spread of the disease in the WB population of South Korea. The results showed that roads and rivers were effective to prevent the spread, reducing the transmission rate to approximately 37% on average. Only a limited level of reduction was indicated via fence‐lines, implying erection of fences might be considered as a temporary measure to delay the spread. This study also revealed that the probability of ASF transmission to adjacent habitats considerably decreased with increasing distance, supporting the slow spatial transmission speed reported from other European countries. Considering that elucidation of ASF dynamics in WB is crucial to mitigate the impact of the disease, we believe this study provides some useful ecological and epidemiological implications to control the disease in future. [ABSTRACT FROM AUTHOR]

Computational modeling plays an important role in a gamut of research fields. In affect research, continuous-time stochastic models are becoming increasingly popular. Recently, a non-linear, continuous-time, stochastic model has been introduced for affect dynamics, called the Affective Ising Model (AIM). The drawback of non-linear models like the AIM is that they generally come with serious computational challenges for parameter estimation and related statistical analyses. The likelihood function of the AIM does not have a closed form expression. Consequently, simulation based or numerical methods have to be considered in order to evaluate the likelihood function. Additionally, the likelihood function can have multiple local minima. Consequently, a global optimization heuristic is required and such heuristics generally require a large number of likelihood function evaluations. In this paper, a Julia software package is introduced that is dedicated to fitting the AIM. The package includes an implementation of a numeric algorithm for fast computations of the likelihood function, which can be run both on graphics processing units (GPU) and central processing units (CPU). The numerical method introduced in this paper is compared to the more traditional Euler-Maruyama method for solving stochastic differential equations. Furthermore, the estimation software is tested by means of a recovery study and estimation times are reported for benchmarks that were run on several computing devices (two different GPUs and three different CPUs). According to these results, a single parameter estimation can be obtained in less than thirty seconds using a mainstream NVIDIA GPU. [ABSTRACT FROM AUTHOR]