|
Abstract:
|
The frequentist variability of Bayesian posterior expectations can provide meaningful measures of uncertainty even when models are misspecified, but classical Gaussian approximations based on the maximum a posteriori estimate can be singular or difficult to compute. These difficulties have prompted some recent authors to bootstrap Markov Chain Monte Carlo (MCMC) procedures. Though naively parallelizable, the bootstrap remains prohibitively computationally intensive, especially for long-running MCMC procedures. We introduce the Bayesian infinitesimal jackknife (IJ), a consistent estimator of the frequentist covariance of an MCMC posterior expectation. Our method is easily computable from a single MCMC chain. We provide an R package to compute the IJ from rstanarm and Stan output. We demonstrate the IJ's accuracy and computational benefits by simulation and by comparison with the bootstrap on models taken from the Stan examples collection.
|
