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The challenging problem of conducting fully Bayesian inference for thereaction rate constants governing stochastic kinetic models (SKMs) isconsidered. Given the challenges underlying this problem, the Markov jumpprocess representation is routinely replaced by an approximation based on asuitable time discretisation of the system of interest. Improving the accuracyof these schemes amounts to using an ever finer discretisation level, which inthe context of the inference problem, requires integrating over the uncertaintyin the process at a predetermined number of intermediate times betweenobservations. Pseudo-marginal Metropolis-Hastings schemes are increasinglyused, since for a given discretisation level, the observed data likelihood canbe unbiasedly estimated using a particle filter. When observations areparticularly informative an auxiliary particle filter can be implemented, byemploying an appropriate construct to push the state particles towards theobservations in a sensible way. Recent work in state-space settings has shownhow the pseudo-marginal approach can be made much more efficient by correlatingthe underlying pseudo-random numbers used to form the likelihood estimate atthe current and proposed values of the unknown parameters. We extend thisapproach to the time-discretised SKM framework by correlating the innovationsthat drive the auxiliary particle filter. We find that the resulting approachoffers substantial gains in efficiency over a standard implementation.

Correlated pseudo-marginal schemes for time-discretised stochastic kinetic models