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The Metropolized Partial Importance Sampling MCMC Mixes Slowly on Minimum Reversal Rearrangement Paths
October-December 2010 (vol. 7 no. 4)
pp. 763-767
István Miklós, Renyi Institute of Mathematical Sciences , Budapest
Bence Mélykúti, University of Oxford, Oxford
Krister Swenson, EPFL, Lausanne
Markov chain Monte Carlo has been the standard technique for inferring the posterior distribution of genome rearrangement scenarios under a Bayesian approach. We present here a negative result on the rate of convergence of the generally used Markov chains. We prove that the relaxation time of the Markov chains walking on the optimal reversal sorting scenarios might grow exponentially with the size of the signed permutations, namely, with the number of syntheny blocks.

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Index Terms:
Stochastic programming, Markov processes, analysis of algorithms and problem complexity, biology and genetics.
István Miklós, Bence Mélykúti, Krister Swenson, "The Metropolized Partial Importance Sampling MCMC Mixes Slowly on Minimum Reversal Rearrangement Paths," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 7, no. 4, pp. 763-767, Oct.-Dec. 2010, doi:10.1109/TCBB.2009.26
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