Math @ Duke

Publications [#328809] of Jonathan C. Mattingly
search arxiv.org.Papers Published
 Johndrow, JE; Mattingly, JC, Coupling and Decoupling to bound an approximating Markov Chain
(July, 2017)
(last updated on 2018/09/19)
Abstract: This simple note lays out a few observations which are well known in many
ways but may not have been said in quite this way before. The basic idea is
that when comparing two different Markov chains it is useful to couple them is
such a way that they agree as often as possible. We construct such a coupling
and analyze it by a simple dominating chain which registers if the two
processes agree or disagree. We find that this imagery is useful when thinking
about such problems. We are particularly interested in comparing the invariant
measures and long time averages of the processes. However, since the paths
agree for long runs, it also provides estimates on various stopping times such
as hitting or exit times. We also show that certain bounds are tight. Finally,
we provide a simple application to a Markov Chain Monte Carlo algorithm and
show numerically that the results of the paper show a good level of
approximation at considerable speed up by using an approximating chain rather
than the original sampling chain.


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