Scalable importance tempering and Bayesian variable selection

We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 81; no. 3; pp. 489 - 517
Main Authors: Zanella, Giacomo, Roberts, Gareth
Format: Journal Article
Language:English
Published: Oxford Wiley 01.07.2019
Oxford University Press
Subjects:
Algorithms
Bayesian analysis
Bayesian theory
Bayesian variable selection; Computational complexity; Gibbs sampling; Importance sampling; Markov chain Monte Carlo sampling; Point mass priors
concrete
equations
Importance sampling
Intuition
Markov analysis
Markov chain
Markov chains
Monte Carlo method
Monte Carlo simulation
probability distribution
Regression analysis
Robustness
Sampling
Statistical methods
Statistics
tempering
ISSN:1369-7412, 1467-9868
Online Access:Get full text
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Summary:We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo methods and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to outperform standard schemes. When applied to Bayesian variable-selection problems, the novel algorithm is orders of magnitude more efficient than available alternative sampling schemes and enables fast and reliable fully Bayesian inferences with tens of thousand regressors.
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ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12316