The Metropolized Partial Importance Sampling MCMC Mixes Slowly on Minimum Reversal Rearrangement Paths
Issue No. 04 - October-December (2010 vol. 7)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TCBB.2009.26
Istvan Miklos , Renyi Institute of Mathematical Sciences , Budapest
Bence Melykuti , 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.
Monte Carlo methods, Bioinformatics, Genomics, Sorting, Genetic mutations, Polynomials, Sampling methods, Bayesian methods, Convergence, Legged locomotion
I. Miklos, B. Melykuti and K. Swenson, "The Metropolized Partial Importance Sampling MCMC Mixes Slowly on Minimum Reversal Rearrangement Paths," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 7, no. 4, pp. 763-767, 2010.