Stability of the Gibbs sampler for Bayesian hierarchical models

DOI10.1214/009053607000000749zbMath1144.65007arXiv0710.4234OpenAlexW2154249701MaRDI QIDQ2477054

Gareth O. Roberts, Omiros Papaspiliopoulos

Publication date: 12 March 2008

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

Full work available at URL: https://arxiv.org/abs/0710.4234

zbMATH Keywords

convergenceparametrizationstate-space modelsBayesian robustnessgeometric ergodicityGaussian process modelscapacitancehierarchical linear modelscollapsed Gibbs sampler

Mathematics Subject Classification ID

Gaussian processes (60G15) Generalized linear models (logistic models) (62J12) Sampling theory, sample surveys (62D05) Monte Carlo methods (65C05)

Related Items

Particle learning and smoothing, Scalable Bayesian computation for crossed and nested hierarchical models, Adaptive Gibbs samplers and related MCMC methods, A comparison of centring parameterisations of Gaussian process-based models for Bayesian computation using MCMC, Nonasymptotic bounds on the estimation error of MCMC algorithms, Gibbs sampling for a Bayesian hierarchical general linear model, A general framework for the parametrization of hierarchical models, A spectral analytic comparison of trace-class data augmentation algorithms and their sandwich variants, Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models, Convergence of Conditional Metropolis-Hastings Samplers, Data transforming augmentation for heteroscedastic models, Variable transformation to obtain geometric ergodicity in the random-walk Metropolis algorithm, Component-wise Markov chain Monte Carlo: uniform and geometric ergodicity under mixing and composition, Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors, Geometric ergodicity of Gibbs samplers for Bayesian general linear mixed models with proper priors

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Random-Effects Models for Longitudinal Data
• Markov chains and stochastic stability
• On rates of convergence of stochastic relaxation for Gaussian and non- Gaussian distributions
• Bayesian image restoration, with two applications in spatial statistics (with discussion)
• The extended exponential power distribution and Bayesian robustness.
• Honest exploration of intractable probability distributions via Markov chain Monte Carlo.
• Rates of convergence for Gibbs sampling for variance component models
• Markov Chains and De-initializing Processes
• Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality
• Posterior expectations for large observations
• Non-Gaussian State-Space Modeling of Nonstationary Time Series
• Model-Based Geostatistics
• Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes
• Partial non-Gaussian state space
• The Collapsed Gibbs Sampler in Bayesian Computations with Applications to a Gene Regulation Problem
• On Gibbs sampling for state space models
• Parameter Expansion for Data Augmentation
• Bayesian Inference for Non-Gaussian Ornstein–Uhlenbeck Stochastic Volatility Processes
• Bayesian Analysis of Linear and Non-Linear Population Models by Using the Gibbs Sampler
• Efficient parametrisations for normal linear mixed models