arXiv subjects

Kushal Kumar Dey

Publications and source records attributed to Kushal Kumar Dey.

3 recordsLinked to original sources

arXiv2017

A Brief Tutorial on Transformation Based Markov Chain Monte Carlo and Optimal Scaling of the Additive Transformation

We consider the recently introduced Transformation-based Markov Chain Monte Carlo (TMCMC) (Dutta and Bhattacharya (2014)), a methodology that is designed to update all the parameters simultaneously using some simple deterministic transformation of a onedimensional random variable drawn from some arbitrary distribution on a relevant support. The additive transformation based TMCMC is similar in spirit to random walk Metropolis, except the fact that unlike the latter, additive TMCMC uses a single draw from a onedimensional proposal distribution to update the high-dimensional parameter. In this paper, we first provide a brief tutorial on TMCMC, exploring its connections and contrasts with various available MCMC methods. Then we study the diffusion limits of additive TMCMC under various set-ups ranging from the product structure of the target density to the case where the target is absolutely continuous with respect to a Gaussian measure; we also consider the additive TMCMC within Gibbs approach for all the above set-ups. These investigations lead to appropriate scaling of the one-dimensional proposal density. We also show that the optimal acceptance rate of additive TMCMC is 0.439 under all the aforementioned set-ups, in contrast with the well-established 0.234 acceptance rate associated with optimal random walk Metropolis algorithms under the same set-ups. We also elucidate the ramifications of our results and clear advantages of additive TMCMC over random walk Metropolis with ample simulation studies and Bayesian analysis of a real, spatial dataset with which 160 unknowns are associated.

stat.ME↗

arXiv2017

On Geometric Ergodicity of Additive and Multiplicative Transformation Based Markov Chain Monte Carlo in High Dimensions

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.

stat.ME↗

arXiv2012

Test for the statistical significance of a treatment effect in the presence of hidden sub-populations

For testing the statistical significance of a treatment effect, we usually compare between two parts of a population, one is exposed to the treatment, and the other is not exposed to it. Standard parametric and nonparametric two-sample tests are often used for this comparison. But direct applications of these tests can yield misleading results, especially when the population has some hidden sub-populations, and the impact of this sub-population difference on the study variables dominates the treatment effect. This problem becomes more evident if these subpopulations have widely different proportions of representatives in the samples taken from these two parts, which are often referred to as the treatment group and the control group. In this article, we make an attempt to overcome this problem. Our propose methods use suitable clustering algorithms to find the hidden sub-populations and then eliminate the sub-population effect by using suitable transformations. Standard two-sample tests, when they are applied on the transformed data, yield better results. Some simulated and real data sets are analyzed to show the utility of the proposed methods.

stat.CO↗