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Title: Fast and consistent inference in compartmental models of epidemics using Poisson approximate likelihoods Authors:  Michael Whitehouse - University of Bristol (United Kingdom) [presenting]
Abstract: Addressing the challenges of scaling up epidemiological inference to complex and heterogeneous populations, we introduce Poisson Approximate Likelihood methods for stochastic compartmental models. A Poisson Approximate Likelihood can be evaluated using only elementary linear-algebraic operations, requires no simulation from the model in order to circumvent the intractability of the true likelihood, and incurs a computational complexity which scales with the number of compartments similarly to that of forwarding Euler discretization of the corresponding ordinary differential equation model. We prove the consistency of the maximizer of the Poisson Approximate Likelihood in the regime where the population size tends to infinity. This appears to be the first consistency result concerning the large population regime for any likelihood or approximate likelihood-based estimator which is applicable across the broad class of compartmental models we consider. Through examples we demonstrate how Poisson Approximate Likelihoods can be: embedded within Delayed Acceptance Particle Markov Chain Monte Carlo to facilitate speed-ups in exact Bayesian inference; applied to an age-structured model of influenza, easily implemented in STAN and compared to ordinary differential equation models; and used to calibrate a large-scale spatial meta-population model of measles transmission.