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Delayed acceptance particle MCMC for exact inference in stochastic kinetic models

机译：延迟接受粒子MCMC用于随机动力学模型的精确推断

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摘要

Recently-proposed particle MCMC methods provide a flexible way of performing Bayesian inference for parameters governing stochastic kinetic models defined as Markov (jump) processes (MJPs). Each iteration of the scheme requires an estimate of the marginal likelihood calculated from the output of a sequential Monte Carlo scheme (also known as a particle filter). Consequently, the method can be extremely computationally intensive. We therefore aim to avoid most instances of the expensive likelihood calculation through use of a fast approximation. We consider two approximations: the chemical Langevin equation diffusion approximation (CLE) and the linear noise approximation (LNA). Either an estimate of the marginal likelihood under the CLE, or the tractable marginal likelihood under the LNA can be used to calculate a first step acceptance probability. Only if a proposal is accepted under the approximation do we then run a sequential Monte Carlo scheme to compute an estimate of the marginal likelihood under the true MJP and construct a second stage acceptance probability that permits exact (simulation based) inference for the MJP. We therefore avoid expensive calculations for proposals that are likely to be rejected. We illustrate the method by considering inference for parameters governing a Lotka-Volterra system, a model of gene expression and a simple epidemic process.
机译：最近提出的粒子MCMC方法为控制定义为马尔可夫（跳跃）过程（MJP）的随机动力学模型的参数提供了执行贝叶斯推断的灵活方法。该方案的每次迭代都需要对从顺序蒙特卡洛方案（也称为粒子滤波器）的输出计算出的边际似然性进行估算。因此，该方法可能需要大量的计算。因此，我们旨在通过使用快速逼近来避免昂贵的似然计算的大多数情况。我们考虑两个近似值：化学朗文方程扩散近似（CLE）和线性噪声近似（LNA）。 CLE下的边际可能性的估计值或LNA下的可处理的边际可能性都可以用来计算第一步接受概率。仅当提案在近似值下被接受时，我们才运行顺序蒙特卡洛方案来计算真实MJP下的边际可能性的估计值，并构建第二阶段接受概率，以允许对MJP进行精确（基于模拟）推断。因此，我们避免为可能被拒绝的提案进行昂贵的计算。我们通过考虑对控制Lotka-Volterra系统的参数，基因表达模型和简单流行过程的推断来说明该方法。

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