Recently-proposed particle MCMC methods provide a flexible way of performingBayesian inference for parameters governing stochastic kinetic models definedas Markov (jump) processes (MJPs). Each iteration of the scheme requires anestimate of the marginal likelihood calculated from the output of a sequentialMonte Carlo scheme (also known as a particle filter). Consequently, the methodcan be extremely computationally intensive. We therefore aim to avoid mostinstances of the expensive likelihood calculation through use of a fastapproximation. We consider two approximations: the chemical Langevin equationdiffusion approximation (CLE) and the linear noise approximation (LNA). Eitheran estimate of the marginal likelihood under the CLE, or the tractable marginallikelihood under the LNA can be used to calculate a first step acceptanceprobability. Only if a proposal is accepted under the approximation do we thenrun a sequential Monte Carlo scheme to compute an estimate of the marginallikelihood under the true MJP and construct a second stage acceptanceprobability that permits exact (simulation based) inference for the MJP. Wetherefore avoid expensive calculations for proposals that are likely to berejected. We illustrate the method by considering inference for parametersgoverning a Lotka-Volterra system, a model of gene expression and a simpleepidemic process.
展开▼
