Model Selection of Stochastic Simulation Algorithm Based on Generalized Divergence Measures
Papa Ngom *
LMA-Laboratoire de Mathématiques Appliquées, Université Cheikh Anta Diop BP 5005 Dakar-Fann Sénégal, Sénégal.
B. Don Bosco Diatta
LMA-Laboratoire de Mathématiques Appliquées, Université Cheikh Anta Diop BP 5005 Dakar-Fann Sénégal, Sénégal.
*Author to whom correspondence should be addressed.
Abstract
We consider the generalized divergence measure approach to compare different simulation strategies such as the Independent Sampler (IS), the Random Walk of Metropolis Hastings (RWMH), the Gibbs Sampler(GS), the Adaptive Metropolis (AM), and Metropolis within Gibbs (MWG). From a selected set of simulation algorithm candidates, the statistical analysis allows us to choose the best strategy in the sense of rate of convergence. We use the informational criteria such as the R´enyi divergence measure Rα(p, q), the Tsallis divergence Tα(p, q), and the -divergence Dα(p, q), where p and q are probability density functions, to show in some examples of synthetic models with target distributions in one dimensional, and two dimensional cases, the consistency and applicability of these -divergence measures for stochastic simulation selection.
Keywords: MCMC methods, Metropolis-Hastings algorithm, Gibbs Sampler, Adaptive Metropolis, Metropolis Within Gibbs, simulation strategy, target density, proposal density, α-divergence measure.