Large Deviations Rate Functions for the Empirical Measure: Explicit Formulas and an Application to Monte Carlo

Liu, Yufei

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Year:: 2013
Contributor:: Liu, Yufei (creator); Dupuis, Paul (Director); Doll, Jimmie (Reader); Ramanan, Kavita (Reader); Brown University. Applied Mathematics (sponsor)
Genre:: theses
Subject:: empirical measure; Markov jump process; Markov chain Monte Carlo; Large deviations
Extent:: xiii, 114 p.
DOI: https://doi.org/10.7301/Z0GB22DT

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Abstract:: In this thesis, we use the large deviations principle to characterize the rate of convergence of the empirical measures of Markov processes. An explicit formula of the large deviations rate function is very useful for this purpose. The main result in this aspect is the Donsker-Varadhan formula for the reversible, continuous time Markov processes. However, it is not applicable to the Markov jump processes, and establishing such a formula is our goal in the first part of this thesis. In the second part, we apply such a formula to a Markov chain Monte Carlo algorithm, the parallel tempering algorithm. By examining the rate function, we arrive at a new class of MCMC algorithm, the infinite swapping algorithm. We then devote the rest of this thesis into the study of infinite swapping algorithm, for both of its theoretical properties and its implementation challenges and solutions.
Notes:: Thesis (Ph.D. -- Brown University (2013)

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Liu, Yufei, "Large Deviations Rate Functions for the Empirical Measure: Explicit Formulas and an Application to Monte Carlo" (2013). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://doi.org/10.7301/Z0GB22DT

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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.
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