Poisson Approximate Likelihood versus the block particle filter for a spatiotemporal measles model

Filtering algorithms for high-dimensional nonlinear non-Gaussian partially observed stochastic processes provide access to the likelihood function and hence enable likelihood-based or Bayesian inference for this methodologically challenging class of models. A novel Poisson approximate likelihood (PAL) filter was introduced by Whitehouse et al.\ (2023). PAL employs a Poisson approximation to conditional densities, offering a fast approximation to the likelihood function for a certain subset of partially observed Markov process models. PAL was demonstrated on an epidemiological metapopulation model for measles, specifically, a spatiotemporal model for disease transmission within and between cities. At face value, Table\ 3 of Whitehouse et al.\ (2023) suggests that PAL considerably out-performs previous analysis as well as an ARMA benchmark model. We show that PAL does not outperform a block particle filter and that the lookahead component of PAL was implemented in a way that introduces substantial positive bias in the log-likelihood estimates. Therefore, the results of Table\ 3 of Whitehouse et al.\ (2023) do not accurately represent the true capabilities of PAL.