Bayesian semiparametric time varying model for count data to study the spread of the COVID-19 cases

Roy, Arkaprava; Karmakar, Sayar

Recent outbreak of the novel corona virus COVID-19 has affected all of our lives in one way or the other. While medical researchers are working hard to find a cure and doctors/nurses to attend the affected individuals, measures such as `lockdown', `stay-at-home', `social distancing' are being implemented in different parts of the world to curb its further spread. To model this spread which is assumed to be a non-stationary count-valued time series, we propose a novel time varying semiparametric AR$(p)$ model for the count valued data of newly affected cases, collected every day and also extend it to propose a novel time varying semiparametric INGARCH model. We calculate posterior contraction rates of the proposed Bayesian methods. Our proposed structures of the models are amenable to Hamiltonian Monte Carlo (HMC) sampling for efficient computation. We show excellent performance in simulations. Our method is then applied on the daily time series data of newly confirmed cases to study its spread through different government interventions.