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The outbreak of Coronavirus Disease 2019 (COVID-19) is an ongoing pandemicaffecting over 200 countries and regions. Inference about the transmissiondynamics of COVID-19 can provide important insights into the speed of diseasespread and the effects of mitigation policies. We develop a novel Bayesianapproach to such inference based on a probabilistic compartmental model usingdata of daily confirmed COVID-19 cases. In particular, we consider aprobabilistic extension of the classical susceptible-infectious-recoveredmodel, which takes into account undocumented infections and allows theepidemiological parameters to vary over time. We estimate the diseasetransmission rate via a Gaussian process prior, which captures nonlinearchanges over time without the need of specific parametric assumptions. Weutilize a parallel-tempering Markov chain Monte Carlo algorithm to efficientlysample from the highly correlated posterior space. Predictions for futureobservations are done by sampling from their posterior predictivedistributions. Performance of the proposed approach is assessed using simulateddatasets. Finally, our approach is applied to COVID-19 data from four states ofthe United States: Washington, New York, California, and Illinois. An R packageBaySIR is made available at https://github.com/tianjianzhou/BaySIR for thepublic to conduct independent analysis or reproduce the results in this paper.

Semiparametric Bayesian Inference for the Transmission Dynamics of COVID-19 with a State-Space Model