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

2025/07/12 by Kai He, He, Kunyang, Edward L. Ionides +2
Mathematics · Medicine · Social Sciences · #COVID-19 epidemiological studies #FOS: Computer and information sciences #Methodology (stat.ME) #Vaccine Coverage and Hesitancy #Virology and Viral Diseases

paper · pdf · doi:10.48550/arxiv.2507.09121

openalex publication_date 2025/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Poisson approximate likelihood compared to the particle filter
• Accelerated Inference for Partially Observed Markov Processes using Automatic Differentiation
• Inference on spatiotemporal dynamics for networks of biological populations
• Approximating optimal SMC proposal distributions in individual-based epidemic models
• Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods
• Iterated Block Particle Filter for High-dimensional Parameter Learning: Beating the Curse of Dimensionality
• Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter
• Can local particle filters beat the curse of dimensionality?
• Strictly Proper Scoring Rules, Prediction, and Estimation

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