Likelihood-free inference and approximate Bayesian computation for stochastic modelling

With increasing model complexity, sampling from the posterior distribution in a Bayesian context becomes challenging. The reason might be that the likelihood function is analytically unavailable or computationally costly to evaluate. In this thesis a fairly new scheme called approximate Bayesian computation is studied which, through simulations from the likelihood function, approximately simulates from the posterior. This is done mainly in a likelihood-free Markov chain Monte Carlo framework and several issues concerning the performance are addressed. Semi-automatic ABC, producing near-sucient summary statistics, is applied to a hidden Markov model and the same scheme is then used, together with a varying bandwidth, to make inference on a real data study under a stochastic Lotka-Volterra model