TY - JOUR

T1 - Efficient particle MCMC for exact inference in stochastic biochemical network models through approximation of expensive likelihoods

AU - Golightly, Andrew

AU - Henderson, Daniel

AU - Sherlock, Christopher

PY - 2015/9

Y1 - 2015/9

N2 - 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.

AB - 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.

KW - Markov jump process

KW - Chemical Langevin equation

KW - Linear noise approximation

KW - Particle MCMC

KW - Delayed acceptance

U2 - 10.1007/s11222-014-9469-x

DO - 10.1007/s11222-014-9469-x

M3 - Journal article

VL - 25

SP - 1039

EP - 1055

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 5

ER -