Particle Methods for Stochastic Differential Equation Mixed Effects Models

Imke Botha, R. Kohn, C. Drovandi
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引用次数: 17

Abstract

Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is a challenging problem. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case, exact inference is possible using the pseudo-marginal method, where the intractable likelihood is replaced by its nonnegative unbiased estimate. A useful application of this idea is particle MCMC, which uses a particle filter estimate of the likelihood. While the exact posterior is targeted by these methods, a naive implementation for SDEMEMs can be highly inefficient. We develop three extensions to the naive approach which exploits specific aspects of SDEMEMs and other advances such as correlated pseudo-marginal methods. We compare these methods on real and simulated data from a tumour xenography study on mice.
随机微分方程混合效应模型的粒子方法
随机微分方程混合效应模型(SDEMEMs)的参数推断是一个具有挑战性的问题。这些模型的分析解决方案很少可用,这意味着可能性也是难以处理的。在这种情况下,使用伪边际方法可以进行精确推断,其中难以处理的似然被其非负无偏估计所取代。这个想法的一个有用的应用是粒子MCMC,它使用粒子滤波估计可能性。虽然这些方法的目标是精确的后验,但对于SDEMEMs的幼稚实现可能非常低效。我们开发了朴素方法的三个扩展,利用了SDEMEMs的特定方面和其他进展,如相关的伪边际方法。我们比较这些方法的真实和模拟数据从肿瘤异种研究的小鼠。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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