Fraunhofer Chalmers Research Centre for Industrial Mathematics
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Approximate Bayesian Computation with Sequential Surrogate Likelihoods
No full textThe 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
