The Monte Carlo Computation Error of Transition Probabilities

  • In many applications one is interested to compute transition probabilities of a Markov chain. This can be achieved by using Monte Carlo methods with local or global sampling points. In this article, we analyze the error by the difference in the $L^2$ norm between the true transition probabilities and the approximation achieved through a Monte Carlo method. We give a formula for the error for Markov chains with locally computed sampling points. Further, in the case of reversible Markov chains, we will deduce a formula for the error when sampling points are computed globally. We will see that in both cases the error itself can be approximated with Monte Carlo methods. As a consequence of the result, we will derive surprising properties of reversible Markov chains.

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Metadaten
Author:Adam Nielsen
Document Type:Article
Parent Title (English):Statistics & Probability Letters
Volume:118
First Page:163
Last Page:170
Publisher:Elsevier
Year of first publication:2016
Preprint:urn:nbn:de:0297-zib-59933
DOI:https://doi.org/10.1016/j.spl.2016.06.011