Browsing by Subject "confidence sets"

Traditional parametric statistical inference methods, such as maximum likelihood and Bayesian inference, cannot be used to learn parameter estimates if the likelihood is intractable, for example due to the complexity of the studied phenomenon. This can be overcome by using likelihood-free inference that is used with simulator-based models to learn parameter estimates. Also, traditional methods used in the estimation of uncertainties related to the parameter estimates typically require a likelihood function, and that is why these methods cannot be applied in likelihood-free inference. In this thesis, we present a novel way to compute confidence sets for parameter estimates obtained from likelihood-free inference using Jensen—Shannon divergence. We consider two test statistics that are based on mean Jensen—Shannon divergence and propose hypothesised asymptotic distributions for them. We test whether these hypothesised distributions can be used in the computation of confidence sets for parameter estimates obtained from likelihood-free inference, and we evaluate the produced confidence sets by studying their frequentist behaviour that is summarised with coverage probabilities. We compare this frequentist behaviour between Jensen —Shannon divergence estimates and confidence sets obtained from grid evaluation of Monte Carlo estimates and from Bayesian optimisation for likelihood-free inference (BOLFI) to the ones obtained from maximum likelihood inference with Wald’s and log likelihood-ratio confidence sets using three different models. We also use a simulator- based model with intractable likelihood to study the proposed confidence sets with BOLFI. In order to study the influence of observations on the parameter estimates and their confidence sets, we conducted these experiments with varying the number of observations. We show that Jensen—Shannon divergence based confidence sets meet the expected frequentist behaviour.