A population Monte Carlo scheme with transformed weights and its application to stochastic kinetic models

摘要

This paper addresses the problem of Monte Carlo approximation of posteriorprobability distributions. In particular, we have considered a recentlyproposed technique known as population Monte Carlo (PMC), which is based on aniterative importance sampling approach. An important drawback of thismethodology is the degeneracy of the importance weights when the dimension ofeither the observations or the variables of interest is high. To alleviate thisdifficulty, we propose a novel method that performs a nonlinear transformationon the importance weights. This operation reduces the weight variation, henceit avoids their degeneracy and increases the efficiency of the importancesampling scheme, specially when drawing from a proposal functions which arepoorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to theestimation of the parameters of a Gaussian mixture model. This is a very simpleproblem that enables us to clearly show and discuss the main features of theproposed technique. As a practical application, we have also considered thepopular (and challenging) problem of estimating the rate parameters ofstochastic kinetic models (SKM). SKMs are highly multivariate systems thatmodel molecular interactions in biological and chemical problems. We introducea particularization of the proposed algorithm to SKMs and present numericalresults.