{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,30]],"date-time":"2026-10-30T21:14:03Z","timestamp":1793394843626,"version":"4.5.0"},"reference-count":62,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T00:00:00Z","timestamp":1688342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Compass\u2014the EPSRC Centre for Doctoral Training in Computational Statistics and Data Science","doi-asserted-by":"publisher","award":["EP\/R018561\/1"],"award-info":[{"award-number":["EP\/R018561\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Bayes for Health"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,29]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad065","type":"journal-article","created":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T19:03:38Z","timestamp":1688411018000},"page":"1173-1203","source":"Crossref","is-referenced-by-count":13,"title":["Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods"],"prefix":"10.1093","volume":"85","author":[{"given":"Michael","family":"Whitehouse","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Bristol , Bristol , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nick","family":"Whiteley","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol , Bristol , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lorenzo","family":"Rimella","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Lancaster , Lancaster , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,7,3]]},"reference":[{"issue":"2","key":"2023092923221252900_qkad065-B1","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.idm.2017.03.001","article-title":"A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis","volume":"2","author":"Allen","year":"2017","journal-title":"Infectious Disease Modelling"},{"key":"2023092923221252900_qkad065-B2","volume-title":"Stochastic epidemic models and their statistical analysis","author":"Andersson","year":"2012"},{"issue":"(1)","key":"2023092923221252900_qkad065-B3","doi-asserted-by":"crossref","first-page":"100415","DOI":"10.1016\/j.epidem.2020.100415","article-title":"An evaluation of Hamiltonian monte carlo performance to calibrate age-structured compartmental SEIR models to incidence data","volume":"33","author":"Andrade","year":"2020","journal-title":"Epidemics"},{"issue":"3","key":"2023092923221252900_qkad065-B4","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1111\/j.1467-9868.2009.00736.x","article-title":"Particle markov chain monte carlo methods","volume":"72","author":"Andrieu","year":"2010","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"2023092923221252900_qkad065-B5","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.epidem.2014.08.001","article-title":"Seven challenges for metapopulation models of epidemics, including households models","volume":"10","author":"Ball","year":"2015","journal-title":"Epidemics"},{"issue":"2","key":"2023092923221252900_qkad065-B6","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.2517-6161.1949.tb00031.x","article-title":"Some evolutionary stochastic processes","volume":"11","author":"Bartlett","year":"1949","journal-title":"Journal of the Royal Statistical Society. 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