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How to Combine Fast Heuristic Markov Chain Monte Carlo with Slow Exact Sampling


 
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1. Title Title of document How to Combine Fast Heuristic Markov Chain Monte Carlo with Slow Exact Sampling
 
2. Creator Author's name, affiliation, country Antar Bandyopadhyay; University of California, Berkeley
 
2. Creator Author's name, affiliation, country David J. Aldous; University of California, Berkeley
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Confidence interval, Exact sampling, Markov chain Monte Carlo.
 
3. Subject Subject classification 60J10, 62M05, 68W20
 
4. Description Abstract Given a probability law $\pi$ on a set $S$ and a function $g : S \rightarrow R$, suppose one wants to estimate the mean $\bar{g} = \int g d\pi$. The Markov Chain Monte Carlo method consists of inventing and simulating a Markov chain with stationary distribution $\pi$. Typically one has no a priori bounds on the chain's mixing time, so even if simulations suggest rapid mixing one cannot infer rigorous confidence intervals for $\bar{g}$. But suppose there is also a separate method which (slowly) gives samples exactly from $\pi$. Using $n$ exact samples, one could immediately get a confidence interval of length $O(n^{-1/2})$. But one can do better. Use each exact sample as the initial state of a Markov chain, and run each of these $n$ chains for $m$ steps. We show how to construct confidence intervals which are always valid, and which, if the (unknown) relaxation time of the chain is sufficiently small relative to $m/n$, have length $O(n^{-1} \log n)$ with high probability.
 
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7. Date (YYYY-MM-DD) 2001-07-28
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1037
 
10. Identifier Digital Object Identifier 10.1214/ECP.v6-1037
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 6
 
12. Language English=en en
 
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