Bayesian logistic regression with the local bouncy particle sampler for COVID-19

A novel coronavirus, called SARS-CoV-2, has caused the outbreak of the pandemic of COVID-19. The global economy, people's health and life have been facing a tremendous threat in COVID-19. This project is to determine some important factors in COVID-19 severity based on 137 Tianjin patients who have been exposed to COVID-19 since January 5, 2020. We fit a logistic regression model and estimate the parameters using standard Markov chain Monte Carlo (MCMC) methods. Due to the weaknesses and limitations of the standard MCMC methods, we then perform model estimation in one special example of a Piecewise Deterministic Markov Process, named the Bouncy Particle Sampler (BPS). This method is also known as a rejection-free and irreversible MCMC, and can draw samples from our target distribution efficiently. One type of the BPS algorithm, the Local Bouncy Particle Sampler (LBPS), has advantages in computational efficiency. We apply the standard MCMC method and the LBPS to our dataset. We conclude that age and Wuhan-related exposures (i.e. people who have lived or traveled from Wuhan) are two important factors in a COVID-19 severity test.