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.
| 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 |
