ANC Seminar: Chris Sherlock (Lancaster)

Delayed acceptance [particle] MCMC for inference on reaction networks.

When conducting Bayesian inference, delayed acceptance (DA) Metropolis-Hastings (MH) algorithms and DA pseudo-marginal MH algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased estimate thereof, but a computationally-cheap approximation is available. A first accept-reject stage is applied, with the cheap approximation substituted for the true posterior in the MH acceptance ratio. Only for those proposals which pass through the first stage is the computationally expensive true posterior (or unbiased estimate thereof) evaluated, with a second accept-reject stage ensuring that detailed balance is satisfied with respect to the intended true posterior. For some reaction networks the Linear Noise Approximation provides a cheap and relatively accurate approximation whereas in other scenarios there is no obvious computationally-cheap surrogate. In such cases a weighted average of previous evaluations of the computationally expensive posterior provides a generic approximation. I will discuss inference for reaction networks using delayed acceptance MCMC in each of the above scenarios.