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title:
A Discrepancy bound of Markov chain quasi-Monte Carlo |
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name:
Rudolf |
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first name:
Daniel
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location/conference:
SPP-JT13
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event_NEW/dateien/SPP-JT13/talks/Rudolf_JT13.pdf |
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abstract:
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of such Markov chain quasi-Monte Carlo methods. We define a push-back discrepancy of the driver sequence and state a close relation to the star-discrepancy. We prove that there exists a deterministic driver sequence such that the discrepancies decrease almost with the Monte Carlo rate $n^{-1/2}$. |
