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Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation

hal.structure.identifierGénétique fonctionnelle des maladies infectieuses - Functional Genetics of Infectious Diseases
hal.structure.identifierInstitut de biologie de l'ENS Paris [IBENS]
dc.contributor.authorNGUYEN-VAN-YEN, Benjamin
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierInstitut de biologie de l'ENS Paris [IBENS]
hal.structure.identifierUnité de modélisation mathématique et informatique des systèmes complexes [Bondy] [UMMISCO]
hal.structure.identifierUniversity of Arizona
dc.contributor.authorCAZELLES, Bernard
dc.date.accessioned2024-04-04T02:48:42Z
dc.date.available2024-04-04T02:48:42Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191763
dc.description.abstractEnWe present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential equation with respect to a Poisson Random Measure (PRM), and how to simulate the process trajectory deterministically from a parameter value and a PRM realisation. This forms the basis of our Data Augmented MCMC, which consists in augmenting parameter space with the unobserved PRM value. The resulting simple Metropolis-Hastings sampler acts as an efficient simulation-based inference method, that can easily be transferred from model to model. Compared with a recent Data Augmentation method based on Gibbs sampling of individual infection histories, PRM-augmented MCMC scales much better with epidemic size and is far more flexible. PRM-augmented MCMC also yields a posteriori estimates of the PRM, that represent process stochasticity, and which can be used to validate the model. If the model is good, the posterior distribution should exhibit no pattern and be close to the PRM prior distribution. We illustrate this by fitting a non-seasonal model to some simulated seasonal case count data. Applied to the Zika epidemic of 2013 in French Polynesia, our approach shows that a simple SEIR model cannot correctly reproduce both the initial sharp increase in the number of cases as well as the final proportion of seropositive. PRM-augmentation thus provides a coherent story for Stochastic Epidemic Model inference, where explicitly inferring process stochasticity helps with model validation.
dc.language.isoen
dc.title.enStochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv2004.10264
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-03033612
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03033612v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=NGUYEN-VAN-YEN,%20Benjamin&DEL%20MORAL,%20Pierre&CAZELLES,%20Bernard&rft.genre=preprint


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