On Additive Transformation based Markov Chain Monte Carlo

In this book, we introduce a single variable transformation based Markov Chain Monte Carlo approach for simulating from distributions with appreciable dimensional and computational complexity. We present here an introduction and theoretical background to this method, focussing mainly on ergodic behavior (in particular geometric ergodicity) and scaling properties under a large class of target distributions. We also propose an R software (tmcmcR) for modeling our algorithm as well adaptive versions of the algorithm and through our wide ranging simulation studies, show the performance gain of this method to standard Random walk based Metropolis Hastings approaches.

Autorentext

I, Kushal Kumar Dey, am a graduate student working on Statistics and Biostatistics at the University of Chicago. My interests include high dimensional data modeling, Markov Chain Monte Carlo, Statistical genetics (RNA-seq and single cell seq data), Phylogenetics, Classification and clustering, Network analysis, Wavelets, Shrinkage methods.