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

TL;DR

This paper critically evaluates the Poisson approximate likelihood (PAL) filter for a spatiotemporal measles model, revealing that it does not outperform the block particle filter and has biases affecting its likelihood estimates.

Contribution

The study challenges previous claims by demonstrating that PAL's performance is comparable to or worse than the block particle filter and identifies biases in PAL's implementation.

Findings

PAL does not outperform the block particle filter.

The lookahead component in PAL introduces positive bias.

Previous results overestimated PAL's effectiveness.

Abstract

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.