Brazilian Journal of Probability and Statistics

On geometric ergodicity of additive and multiplicative transformation-based Markov Chain Monte Carlo in high dimensions

Kushal Kr. Dey and Sourabh Bhattacharya

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Recently Dutta and Bhattacharya (Statistical Methodology 16 (2014) 100–116) 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, assuming that the target distribution is multi-dimensional and belongs to the super-exponential family; we also illustrate their efficiency in practice with simulation studies.

Article information

Braz. J. Probab. Stat., Volume 30, Number 4 (2016), 570-613.

Received: July 2014
Accepted: July 2015
First available in Project Euclid: 13 December 2016

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Acceptance rate geometric ergodicity high dimension mixture proposal distribution transformation-based Markov Chain Monte Carlo


Dey, Kushal Kr.; Bhattacharya, Sourabh. On geometric ergodicity of additive and multiplicative transformation-based Markov Chain Monte Carlo in high dimensions. Braz. J. Probab. Stat. 30 (2016), no. 4, 570--613. doi:10.1214/15-BJPS295.

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