Model selection of stochastic simulation algorithm based on generalized divergence measures

الأصل · EN

MCMC methods (Monte Carlo Markov Chain) are a class of methods used to perform simulations per a probability distribution P. These methods are often used when we have difficulties to directly sample per a given probability distribution P. This distribution is then considered as a target and generates a Markov chain (Xₙ)n that, when n is large we have Xₙ P. These MCMC methods consist of several simulation strategies including the Independent Sampler (IS), the Random Walk of Metropolis Hastings (RWMH), the Gibbs sampler, the Adaptive Metropolis (AM) and Metropolis Within Gibbs (MWG) strategy. Each of these strategies can generate a Markov chain and is associated with a convergence speed. It is interesting, with a given target law, to compare several simulation strategies for determining the best. Chauveau and Vandekerkhove Chauv2007 have compared IS and RWMH strategies using the Kullback-Leibler divergence measure. In our article we will compare our five simulation methods already mentioned using generalized divergence measures. These divergence measures are taken in family of α-divergence measures Cichocki2010, with a parameter α. This is the Rényi divergence, Tsallis divergence and Dα divergence.