Open AccessMarkov Chain Confidence Intervals and Biases
Author(s) -
Yu Hang Jiang,
Tong Liu,
Zhiya Lou,
Jeffrey S. Rosenthal,
Shanshan Shangguan,
Fei Wang,
Zixuan Wu
Publication year - 2021
Publication title -
international journal of statistics and probability
Language(s) - English
Resource type - Journals
eISSN - 1927-7040
pISSN - 1927-7032
DOI - 10.5539/ijsp.v11n1p29
Subject(s) - mathematics , ergodicity , markov chain monte carlo , markov chain , delta method , simple (philosophy) , limit (mathematics) , confidence interval , asymptotic analysis , central limit theorem , statistics , monte carlo method , mathematical analysis , estimator , philosophy , epistemology
We derive explicit asymptotic confidence intervals for any Markov chain Monte Carlo (MCMC) algorithm with finite asymptotic variance, started at any initial state, without requiring a Central Limit Theorem nor reversibility nor geometric ergodicity nor any bias bound. We also derive explicit non-asymptotic confidence intervals assuming bounds on the bias or first moment, or alternatively that the chain starts in stationarity. We relate those non-asymptotic bounds to properties of MCMC bias, and show that polynomially ergodicity implies certain bias bounds. We also apply our results to several numerical examples. It is our hope that these results will provide simple and useful tools for estimating errors of MCMC algorithms when CLTs are not available.