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Register a new userA practical sequential stopping rule for high-dimensional MCMC and its application to spatial-temporal Bayesian models
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Added by
James M. Flegal
Publication date
2014
fields
Mathematical Statistics
and research's language is
English
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A current challenge for many Bayesian analyses is determining when to terminate high-dimensional Markov chain Monte Carlo simulations. To this end, we propose using an automated sequential stopping procedure that terminates the simulation when the computational uncertainty is small relative to the posterior uncertainty. Such a stopping rule has previously been shown to work well in settings with posteriors of moderate dimension. In this paper, we illustrate its utility in high-dimensional simulations while overcoming some current computational issues. Further, we investigate the relationship between the stopping rule and effective sample size. As examples, we consider two complex Bayesian analyses on spatially and temporally correlated datasets. The first involves a dynamic space-time model on weather station data and the second a spatial variable selection model on fMRI brain imaging data. Our results show the sequential stopping rule is easy to implement, provides uncertainty estimates, and performs well in high-dimensional settings.
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We introduce and illustrate through numerical examples the R package texttt{SIHR} which handles the statistical inference for (1) linear and quadratic functionals in the high-dimensional linear regression and (2) linear functional in the high-dimensional logistic regression. The focus of the proposed algorithms is on the point estimation, confidence interval construction and hypothesis testing. The inference methods are extended to multiple regression models. We include real data applications to demonstrate the packages performance and practicality.
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