Approximate Bayesian computation with applications to time series data and spread of covid-19

Abstract

Bayesian statistical methods are one of the most popular tools for parameter inference. However, due to their dependence on a well defined and analytically tractable likelihood function, they are not always applicable to models of arbitrary complexity. Approximate Bayesian computation (ABC) methods counteract this by introducing a Bayesian framework utilising model simulations to bypass the need for a closed-form likelihood function. In this thesis we explore two ABC methods, the ABC rejection algorithm and the sequential Monte Carlo ABC (SMCABC) algorithm. We use them to infer parameters for the autoregressive AR(2) model, the Lotka-Volterra model for predators and prey, and the SIR-model for modeling the spread of Covid19 in Sweden. Subsequently, we compare the generated parameter distributions to the exact posteriors produced by the more well-known Metropolis-Hastings algorithm. The results indicate that the ABC methods produce posterior distributions comparable to those generated by the Metropolis-Hastings algorithm, that the SMC-ABC algorithm is more computationally efficient than the ABC rejection algorithm, and that the resulting posterior distributions are quite independent of the choice of prior.