Model Selection of Stochastic Simulation Algorithm Based on Generalized Divergence Measures

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.