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Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models

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 (R...

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Autores principales: Liang, Xitong, Livingstone, Samuel, Griffin, Jim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10528396/
https://www.ncbi.nlm.nih.gov/pubmed/37761609
http://dx.doi.org/10.3390/e25091310
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author Liang, Xitong
Livingstone, Samuel
Griffin, Jim
author_facet Liang, Xitong
Livingstone, Samuel
Griffin, Jim
author_sort Liang, Xitong
collection PubMed
description 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.
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spelling pubmed-105283962023-09-28 Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models Liang, Xitong Livingstone, Samuel Griffin, Jim Entropy (Basel) Article 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. MDPI 2023-09-08 /pmc/articles/PMC10528396/ /pubmed/37761609 http://dx.doi.org/10.3390/e25091310 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Liang, Xitong
Livingstone, Samuel
Griffin, Jim
Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models
title Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models
title_full Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models
title_fullStr Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models
title_full_unstemmed Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models
title_short Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models
title_sort adaptive mcmc for bayesian variable selection in generalised linear models and survival models
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10528396/
https://www.ncbi.nlm.nih.gov/pubmed/37761609
http://dx.doi.org/10.3390/e25091310
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