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 L2 norm between the true transition probabilities and t...

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Bibliographic Details
Published in:Statistics & probability letters Vol. 118; pp. 163 - 170
Main Author: Nielsen, Adam
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2016
Subjects:
Computation error
Markov operator
Measurable state space
Monte Carlo methods
Reversible Markov chain
Monte Carlo methods
Reversible Markov chain
Measurable state space
Markov operator
Computation error
ISSN:0167-7152, 1879-2103
Online Access:Get full text
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Summary: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 L2 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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2016.06.011