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.