Approximate Bayesian Computation with Sequential Surrogate Likelihoods

The purpose of this thesis was to implement, analyze, and possibly expand a Bayesian inference method related to approximate Bayesian computation (ABC). This method was initially suggested by the supervisor and was given the working name approximate Bayesian computation with sequential surrogate likelihoods (ABC-SSL). The underlying idea for the method was to replace ABC distances with predicted distances obtained using some regression technique, thus circumventing generation of synthetic datasets from the Bayesian model. These predictions would then be improved in a sequential manner, leading to a significant decrease of computational cost for parameter inference. The literature on ABC was studied in search of similar techniques with the intent of finding suitable methods to be compared to ABC-SSL in a simulation study. Gaussian process regression was chosen to model the distances due to the need for flexibility. An interpretation and generalization of the preliminary ABC-SSL method was given, relating it to some of the methods found in the literature. The simulation study was constructed with three examples, including one of the standard models in the ABC literature, the g-and-k distribution. These examples were chosen to give an understanding of potential use of the method. Due to lack of promising results of these numerical results, the complexity of the tested models were kept low. No conclusive evidence was found for the inference method to be suitable for practical use in its current state due to questionable asymptotic properties and difficulties in finding appropriate surrogate models. One possible application is to use the proposed technique to find regions of suspected high posterior probability of the parameter space to be used in combination with traditional ABC methods. Another possibility is to consider Bayesian optimization problems, although such problems were not explicitly investigated in this thesis