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

机译：具有权重的种群蒙特卡洛方案及其在随机动力学模型中的应用

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摘要

This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from 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 simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are 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.
机译：本文讨论了后验概率分布的蒙特卡罗近似。特别是，我们考虑基于迭代重要性抽样（IS）方法的人口蒙特卡洛（PMC）技术。该方法的一个重要缺点是，当观测值或相关变量的维数很高时，重要性权重（IW）就会退化。为了减轻这一困难，我们提出了一种对IW进行非线性变换的新方法。此操作减少了权重变化，因此避免了退化，并提高了IS方案的效率，尤其是在从提议函数中提取时，该提议函数很难适应真实的后验。为了说明起见，我们将提出的算法应用于高斯混合模型参数的估计。这是一个简单的问题，使我们能够讨论所提出技术的主要特征。在实际应用中，我们还考虑了估计随机动力学模型（SKM）的速率参数的难题。 SKM是用于模拟生物学和化学问题中分子相互作用的多元系统。我们将提出的算法具体化为SKM，并给出数值结果。

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