Convergence complexity analysis of Albert and Chib's algorithm for Bayesian probit regression

DOI10.1214/18-AOS1749zbMath1467.60053arXiv1712.08867OpenAlexW2798428389MaRDI QIDQ2313288

James P. Hobert, Qian Qin

Publication date: 18 July 2019

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.08867

zbMATH Keywords

Markov chain Monte Carlogeometric ergodicitydrift conditionminorization conditionhigh dimensional inferencelarge \(p\)-small \(n\)

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Discrete-time Markov processes on general state spaces (60J05)

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Cites Work

• Unnamed Item
• A study of variable selection using \(g\)-prior distribution with ridge parameter
• Convergence properties of Gibbs samplers for Bayesian probit regression with proper priors
• On the computational complexity of high-dimensional Bayesian variable selection
• Gibbs sampling, exponential families and orthogonal polynomials
• Markov chain Monte Carlo: can we trust the third significant figure?
• On Monte Carlo methods for Bayesian multivariate regression models with heavy-tailed errors
• Approximate counting, uniform generation and rapidly mixing Markov chains
• Computable bounds for geometric convergence rates of Markov chains
• Geometric ergodicity and hybrid Markov chains
• Honest exploration of intractable probability distributions via Markov chain Monte Carlo.
• Bounds on regeneration times and convergence rates for Markov chains
• Renewal theory and computable convergence rates for geometrically erdgodic Markov chains
• Convergence complexity analysis of Albert and Chib's algorithm for Bayesian probit regression
• High-dimensional Bayesian inference via the unadjusted Langevin algorithm
• Geometric ergodicity of Gibbs samplers in Bayesian penalized regression models
• Nonasymptotic bounds on the estimation error of MCMC algorithms
• Markov Chains and De-initializing Processes
• Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
• Geometric L² and ^{L1 convergence are equivalent for reversible Markov chains}
• Markov Chains and Stochastic Stability
• Variable Selection in Regression Mixture Modeling for the Discovery of Gene Regulatory Networks
• Markov-chain monte carlo: Some practical implications of theoretical results
• On the geometric ergodicity of hybrid samplers
• Propriety of posterior distribution for dichotomous quantal response models
• Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo
• Convergence Rates and Asymptotic Standard Errors for Markov Chain Monte Carlo Algorithms for Bayesian Probit Regression
• MCMC for Imbalanced Categorical Data
• Bayesian Analysis of Binary and Polychotomous Response Data
• Geometric Ergodicity of van Dyk and Meng's Algorithm for the Multivariate Student'stModel
• Complexity results for MCMC derived from quantitative bounds