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BAYESIAN ANALYSIS OF THE PREDICTIVE DISTRIBUTION OF THE SIR MODELS
Keywords:
the posterior predictive distribution, the posterior distribution, the SIR epidemic model, major epidemic.DOI:
https://doi.org/10.17654/0972361722024Abstract
This paper is concerned with the behavior of the posterior predictive distribution when the sample size is large. The main focus is on the limiting behavior of the posterior predictive distribution of the susceptible-infected-recovered (SIR) epidemic model. In particular, a general result regarding the behavior of the posterior predictive distribution is obtained. Furthermore, the convergence of the posterior predictive distribution of the Markovian SIR model is explored. We prove, under certain assumptions, that the limiting behavior of the posterior predictive distribution of the Markovian SIR epidemic model depends on the limiting behavior of the posterior distributions of the model parameters which converge to mixture distributions. For a major outbreak, they converge to Dirac delta functions concentrated around the true values of the parameters while for a minor outbreak they converge to other specified gamma distributions.
Received: January 12, 2022
Accepted: March 3, 2022
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