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The Monte Carlo computation error of transition probabilities

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  • Nielsen, Adam

Abstract

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.

Suggested Citation

  • Nielsen, Adam, 2016. "The Monte Carlo computation error of transition probabilities," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 163-170.
    • Handle: RePEc:eee:stapro:v:118:y:2016:i:c:p:163-170
    DOI: 10.1016/j.spl.2016.06.011
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    References listed on IDEAS

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    1. Baxter, J. R. & Rosenthal, Jeffrey S., 1995. "Rates of convergence for everywhere-positive Markov chains," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 333-338, March.
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    Cited by:

    1. Lu, Cheng & Teng, Da & Chen, Jun-Yu & Fei, Cheng-Wei & Keshtegar, Behrooz, 2023. "Adaptive vectorial surrogate modeling framework for multi-objective reliability estimation," Reliability Engineering and System Safety, Elsevier, vol. 234(C).

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