Local Consistency of Markov Chain Monte Carlo Methods

In this paper, we introduce the notion of efficiency (consistency) and examine some asymptotic properties of Markov chain Monte Carlo methods. We apply these results to the data augmentation (DA) procedure for independent and identically distributed observations. More precisely, we show that if both the sample size and the running time of the DA procedure tend to infinity the empirical distribution of the DA procedure tends to the posterior distribution. This is a local property of the DA procedure, which may be, in some cases, more helpful than the global properties to describe its behavior. The advantages of using the local properties are the simplicity and the generality of the results. The local properties provide useful insight into the problem of how to construct efficient algorithms.Comment: 12 page

ParaHaplo 3.0: A program package for imputation and a haplotype-based whole-genome association study using hybrid parallel computing

<p>Abstract</p> <p>Background</p> <p>Use of missing genotype imputations and haplotype reconstructions are valuable in genome-wide association studies (GWASs). By modeling the patterns of linkage disequilibrium in a reference panel, genotypes not directly measured in the study samples can be imputed and used for GWASs. Since millions of single nucleotide polymorphisms need to be imputed in a GWAS, faster methods for genotype imputation and haplotype reconstruction are required.</p> <p>Results</p> <p>We developed a program package for parallel computation of genotype imputation and haplotype reconstruction. Our program package, ParaHaplo 3.0, is intended for use in workstation clusters using the Intel Message Passing Interface. We compared the performance of ParaHaplo 3.0 on the Japanese in Tokyo, Japan and Han Chinese in Beijing, and Chinese in the HapMap dataset. A parallel version of ParaHaplo 3.0 can conduct genotype imputation 20 times faster than a non-parallel version of ParaHaplo.</p> <p>Conclusions</p> <p>ParaHaplo 3.0 is an invaluable tool for conducting haplotype-based GWASs. The need for faster genotype imputation and haplotype reconstruction using parallel computing will become increasingly important as the data sizes of such projects continue to increase. ParaHaplo executable binaries and program sources are available at <url>http://en.sourceforge.jp/projects/parallelgwas/releases/</url>.</p