Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods

Michael Whitehouse*, Nick Whiteley, Lorenzo Rimella

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
1 Downloads (Pure)


Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson approximate likelihood (PAL) methods. In contrast to the popular ordinary differential equation (ODE) approach to compartmental modelling, in which a large population limit is used to motivate a deterministic model, PALs are derived from approximate filtering equations for finite-population, stochastic compartmental models, and the large population limit drives consistency of maximum PAL estimators. Our theoretical results appear to be the first likelihood-based parameter estimation consistency results which apply to a broad class of partially observed stochastic compartmental models and address the large population limit. PALs are simple to implement, involving only elementary arithmetic operations and no tuning parameters, and fast to evaluate, requiring no simulation from the model and having computational cost independent of population size. Through examples we demonstrate how PALs can be used to: fit an age-structured model of influenza, taking advantage of automatic differentiation in Stan; compare over-dispersion mechanisms in a model of rotavirus by embedding PALs within sequential Monte Carlo; and evaluate the role of unit-specific parameters in a meta-population model of measles.
Original languageEnglish
Pages (from-to)1173-1203
JournalJournal of the Royal Statistical Society: Series B
Issue number4
Early online date23 Jul 2023
Publication statusPublished - 1 Sept 2023


  • stat.ME
  • cs.LG


Dive into the research topics of 'Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods'. Together they form a unique fingerprint.

Cite this