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Markov Chain Monte Carlo methods have emerged as one of the premier approaches to estimating posterior distributions for use in Bayesian computations. Unfortunately, these methods often suffer from slow run times when the data become large or when the parameter values come from complex distributions. This speed issue has prevented MCMC analysis from being used to solve some of the most interesting problems for which its technique is a good fit. We used the Multiple-Try Metropolis variant of the basic Metropolis Hastings algorithm, which trades off running more parallel likelihood calculations in favor of a higher acceptance rate and faster convergence compared to traditional MCMC. We optimized our algorithm to parallelize it and to take advantage of GPU processing. We applied our approach to parameter estimation for a Susceptible-Exposed-Infectious-Removed (SEIR) model and forecasting new cases of COVID-19. In comparison to a fully parallelized CPU implementation, using a single GPU to execute the simulations resulted in more than a 13x speedup in wall clock time, running on multiple GPUs resulted in a 36.3x speedup in wall clock time, and using a cloud-based server consisting of 8 GPUs resulted in a 56.5x speedup in wall clock time. Our approach shows that MCMC methods can be utilized to tackle problems that were previously thought to be too computationally intensive and slow.

GPU Accelerated Parallel Processing for Large-Scale Monte Carlo Analysis: COVID-19 Parameter Estimation and New Case Forecasting