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Developments and Applications of Markov Chain Monte Carlo in Bayesian Inference

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 28 February 2025 | Viewed by 2825

Special Issue Editors


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Guest Editor
Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos 13566-590, Brazil
Interests: Bayesian methods; Markov chain Monte Carlo methods and applications

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Guest Editor
1. Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, K. Donelaičio g. 73, 44249 Kaunas, Lithuania
2. Lithuanian Energy Institute, Breslaujos St. 3, 44403 Kaunas, Lithuania
Interests: probabilistic risk assessment; complex systems; Bayesian inference; artificial intelligence; big data analytics; data mining; machine learning; artificial neural networks
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Special Issue Information

Dear Colleagues,

Markov Chain Monte Carlo (MCMC) algorithms are now widely applied in Bayesian statistics for sampling from the posterior distribution of all unknown quantities in a model, for which direct sampling would be difficult. There are many situations, however, where it is impractical or even impossible to draw the samples, e.g., with massive datasets or in the case of intractable posterior and likelihood models. Further, the efficiency and applicability of MCMC depend on how the underlying issue of sampling is taken into account when designing the transition kernel, especially for target distributions with complex dependence structures or with time dependence. In this case, the practical implementation, application, and accuracy of relevant result estimates may suffer from a very slow and sparse exploration of the target distribution.

This Special Issue invites the submission of papers that aim to advance computational developments and innovations in Bayesian statistics, with particular emphasis on Markov chain Monte Carlo methods and their application variants. Papers are expected to contribute to the design of efficient methods and algorithms or improve existing ones with possible demonstrations in challenging applications (e.g., in multidisciplinary technology, industry, or health science). Therefore, this Special Issue welcomes both novel methodological and application-focused contributions to the area of MCMC. Thus, we are seeking contributions and novel MCMC applications, including, but not limited to, the following topics: MCMC in Bayesian inference, Bayesian distributional regression and Bayesian latent class models, MCMC application for probabilistic assessment, uncertainty and sensitivity analysis, anomaly detection, reliability and safety estimation, extreme event analysis, testing or detection quality estimation, big data analytics, information integration, and data fusion applications.

Dr. Ricardo Sandes Ehlers
Prof. Dr. Robertas Alzbutas
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Bayesian statistics
  • Markov chain Monte Carlo
  • Bayesian inference applications
  • Bayesian distributional regression
  • Bayesian latent class models

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Published Papers (2 papers)

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Research

17 pages, 468 KiB  
Article
A Semiparametric Bayesian Approach to Heterogeneous Spatial Autoregressive Models
by Ting Liu, Dengke Xu and Shiqi Ke
Entropy 2024, 26(6), 498; https://doi.org/10.3390/e26060498 - 7 Jun 2024
Viewed by 708
Abstract
Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed [...] Read more.
Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis–Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method. Full article
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23 pages, 777 KiB  
Article
Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models
by Xitong Liang, Samuel Livingstone and Jim Griffin
Entropy 2023, 25(9), 1310; https://doi.org/10.3390/e25091310 - 8 Sep 2023
Cited by 2 | Viewed by 1419
Abstract
Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions to the marginal likelihood. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach [...] Read more.
Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions to the marginal likelihood. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach can be employed to jointly sample models and coefficients, but the effective design of the trans-dimensional jumps of RJMCMC can be challenging, making it hard to implement. Alternatively, the marginal likelihood can be derived conditional on latent variables using a data-augmentation scheme (e.g., Pólya-gamma data augmentation for logistic regression) or using other estimation methods. However, suitable data-augmentation schemes are not available for every generalised linear model and survival model, and estimating the marginal likelihood using a Laplace approximation or a correlated pseudo-marginal method can be computationally expensive. In this paper, three main contributions are presented. Firstly, we present an extended Point-wise implementation of Adaptive Random Neighbourhood Informed proposal (PARNI) to efficiently sample models directly from the marginal posterior distributions of generalised linear models and survival models. Secondly, in light of the recently proposed approximate Laplace approximation, we describe an efficient and accurate estimation method for marginal likelihood that involves adaptive parameters. Additionally, we describe a new method to adapt the algorithmic tuning parameters of the PARNI proposal by replacing Rao-Blackwellised estimates with the combination of a warm-start estimate and the ergodic average. We present numerous numerical results from simulated data and eight high-dimensional genetic mapping data-sets to showcase the efficiency of the novel PARNI proposal compared with the baseline add–delete–swap proposal. Full article
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

 
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