Error bounds of MCMC for functions with unbounded stationary variance

Daniel Rudolf and Nikolaus Schweizer

Statistics & Probability Letters, 2015, vol. 99, issue C, 6-12

Abstract: We prove explicit error bounds for Markov chain Monte Carlo (MCMC) methods to compute expectations of functions with unbounded stationary variance. We assume that there is a p∈(1,2) so that the functions have finite Lp-norm. For uniformly ergodic Markov chains we obtain error bounds with the optimal order of convergence n1/p−1 and if there exists a spectral gap we almost get the optimal order. Further, a burn-in period is taken into account and a recipe for choosing the burn-in is provided.

Keywords: Markov chain Monte Carlo; Absolute mean error; Uniform ergodicity; Spectral gap (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2014.07.035

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