5994
2016
eng
163
170
118
article
Elsevier
0
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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.
Statistics & Probability Letters
10.1016/j.spl.2016.06.011
yes
urn:nbn:de:0297-zib-59933
Adam Nielsen
Adam Nielsen
Numerical Mathematics
Computational Molecular Design
BMS-Nielsen
EyeTracking
NonequiMSM
SFB1114-A5