A hierarchical Bayesian approach for modeling the evolution of the 7-day moving average of the number of deaths by COVID-19

In this paper, we propose a hierarchical Bayesian approach for modeling the evolution of the 7-day moving average for the number of deaths due to COVID-19 in a country, state or city. The proposed approach is based on a Gaussian process regression model. The main advantage of this model is that it assumes that a nonlinear function f used for modeling the observed data is an unknown random parameter in opposite to usual approaches that set up f as being a known mathematical function. This assumption allows the development of a Bayesian approach with a Gaussian process prior over f. In order to estimate the parameters of interest, we develop an MCMC algorithm based on the Metropolis-within-Gibbs sampling algorithm. We also present a procedure for making predictions. The proposed method is illustrated in a case study, in which, we model the 7-day moving average for the number of deaths recorded in the state of São Paulo, Brazil. Results obtained show that the proposed method is very effective in modeling and predicting the values of the 7-day moving average.