Bayesian Emulation and Calibration of a Dynamic Epidemic Model for A/H1N1 Influenza

In this article, we develop a Bayesian framework for parameter estimation of a computationally expensive dynamic epidemic model using time series epidemic data. Specifically, we work with a model for A/H1N1 influenza, which is implemented as a deterministic computer simulator, taking as input the underlying epidemic parameters and calculating the corresponding time series of reported infections. To obtain Bayesian inference for the epidemic parameters, the simulator is embedded in the likelihood for the reported epidemic data. However, the simulator is computationally slow, making it impractical to use in Bayesian estimation where a large number of simulator runs is required. We propose an efficient approximation to the simulator using an emulator, a statistical model that combines a Gaussian process (GP) prior for the output function of the simulator with a dynamic linear model (DLM) for its evolution through time. This modeling framework is both flexible and tractable, resulting in efficient posterior inference through Markov chain Monte Carlo (MCMC). The proposed dynamic emulator is then used in a calibration procedure to obtain posterior inference for the parameters of the influenza epidemic.