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Markov Chain Monte Carlo for Bayesian Inference

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

Deadline for manuscript submissions: closed (15 March 2024) | Viewed by 1381

Special Issue 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

Special Issue Information

Dear Colleagues,

Markov Chain Monte Carlo (MCMC) algorithms are now routinely used 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 for intractable likelihood models. Further, the efficiency of MCMC depends on how the underlying geometry of the problem is taken into account when designing the transition kernel, especially for target distributions with complex dependence structures. In this case, a naive implementation may suffer from a very slow exploration of the target distribution.

This Special Issue invites the submission of papers that aim at advancing computational developments in Bayesian statistics, with particular emphasis on Markov chain Monte Carlo methods and their variants. Papers are expected to contribute to the design of efficient algorithms or improve existing ones, in challenging applications. Therefore, the Special Issue welcomes both novel methodological and application-focused contributions to the area.

Dr. Ricardo Sandes Ehlers
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

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
  • Metropolis–Hastings
  • Gibbs sampler
  • Hamiltonian Monte Carlo

Published Papers (1 paper)

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Research

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 - 08 Sep 2023
Viewed by 925
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
(This article belongs to the Special Issue Markov Chain Monte Carlo for Bayesian Inference)
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