Repository: Freie Universit├Ąt Berlin, Math Department

The Monte Carlo computation error of transition probabilities

Nielsen, A. (2016) The Monte Carlo computation error of transition probabilities. Statistics & Probability Letters, 118 . pp. 163-170. ISSN 0167-7152

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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.

Item Type:Article
Uncontrolled Keywords:Reversible Markov chain; Monte Carlo methods; Computation error; Measurable state space; Markov operator
Subjects:Mathematical and Computer Sciences
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:1983
Deposited By: BioComp Admin
Deposited On:25 Nov 2016 09:35
Last Modified:25 Nov 2016 09:35

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