  Recently Dutta and Bhattacharya (2013) introduced a novel Markov Chain Monte
Carlo methodology that can simultaneously update all the components of high
dimensional parameters using simple deterministic transformations of a
one-dimensional random variable drawn from any arbitrary distribution defined
on a relevant support. The methodology, which the authors refer to as
Transformation-based Markov Chain Monte Carlo (TMCMC), greatly enhances
computational speed and acceptance rate in high-dimensional problems. Two
significant transformations associated with TMCMC are additive and
multiplicative transformations. Combinations of additive and multiplicative
transformations are also of much interest. In this work we investigate
geometric ergodicity associated with additive and multiplicative TMCMC, along
with their combinations, and illustrate their efficiency in practice with
simulation studies.
