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Fixed Precision MCMC Estimation by Median of Products of Averages
- Part of
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- Journal:
- Journal of Applied Probability / Volume 46 / Issue 2 / June 2009
- Published online by Cambridge University Press:
- 14 July 2016, pp. 309-329
- Print publication:
- June 2009
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- Article
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The standard Markov chain Monte Carlo method of estimating an expected value is to generate a Markov chain which converges to the target distribution and then compute correlated sample averages. In many applications the quantity of interest θ is represented as a product of expected values, θ = µ1 ⋯ µk, and a natural estimator is a product of averages. To increase the confidence level, we can compute a median of independent runs. The goal of this paper is to analyze such an estimator
, i.e. an estimator which is a ‘median of products of averages’ (MPA). Sufficient conditions are given for to have fixed relative precision at a given level of confidence, that is, to satisfy 
. Our main tool is a new bound on the mean-square error, valid also for nonreversible Markov chains on a finite state space.
, i.e. an estimator which is a ‘median of products of averages’ (MPA). Sufficient conditions are given for 
. Our main tool is a new bound on the mean-square error, valid also for nonreversible Markov chains on a finite state space.