On Mixing Time for Some Markov Chain Monte Carlo

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Mohammad Taheri, Sara | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45508 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Alishahi, Kasra
Abstract:
Markov chains are memoryless stochastic processes that undergoes transitions from one state to another state on a state space having the property that, given the present,the future is conditionally independent of the past. Under general conditions, the markov chain has a stationary distribution and the probability distribution of the markov chain, independent of the staring state, converges to it’s stationary distribution.
We use this fact to construct markov chain monte carlo, which are a class of algorithms for sampling from probability distributions based on constructing a markov chain that has the desired distribution as its stationary distribution. The state of a chain after a large number of steps is then used as a sample of the desired distribution. One important question is estimating the time a markov chain needs to be close to its stationary distribution which we call mixing time. In this thesis we try to find the mixing time for some special kinds of markov chains
Keywords:
Mixing Time ; Markov Chain ; Coupling ; Markov Chain Monte Carlo ; Total Variation Distance