5993
eng
reportzib
0
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2016-07-22
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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.
1438-0064
urn:nbn:de:0297-zib-59933
appeared in: Statistics & Probability Letters 118 (2016) pp. 163-170.
Adam Nielsen
Adam Nielsen
ZIB-Report
16-37
eng
uncontrolled
Reversible Markov chain
eng
uncontrolled
Monte Carlo methods
eng
uncontrolled
Computation error
eng
uncontrolled
Measurable state space
eng
uncontrolled
Markov operator
NUMERICAL ANALYSIS
PROBABILITY AND STATISTICS
Mathematical methods in physics
DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
NUMERICAL ANALYSIS
Numerical Mathematics
Computational Molecular Design
BMS-Nielsen
EyeTracking
NonequiMSM
SFB1114-A5
https://opus4.kobv.de/opus4-zib/files/5993/MonteCarloError.pdf