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

Abstract

This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative importance sampling approach. An important drawback of this methodology is the degeneracy of the importance weights when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a novel method that performs a nonlinear transformation on the importance weights. This operation reduces the weight variation, hence it avoids their degeneracy and increases the efficiency of the importance sampling scheme, specially when drawing from a proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a very simple problem that enables us to clearly show and discuss the main features of the proposed technique. As a practical application, we have also considered the popular (and challenging) problem of estimating the rate parameters of stochastic kinetic models (SKM). SKMs are highly multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results.