| Approximate Bayesian computation applies the Bayesian framework to the analysis of a complex system, where the likelihood function is intractable or hard to compute but simulations from the system are available at reasonable cost. The main idea of approximate Bayesian computation is to match simulation data to the observed data as accurately as possible. Due to the complexity of data in many problems, summary statistics are used for the comparison between simulation data and the observed data. Given a set of candidate summary statistics in a problem, selection of the most informative subset of summary statistics is essential to the successful application of the approximate Bayesian computation framework. Existing summary statistic selection methods suffer from heavy computation overheads and are difficult to apply to problems with a relatively large set of summary statistics. This thesis proposes a new method, the ellipse search method, to reformulate and accelerate the search process for the most informative subset of summary statistics. In the existing summary statistics selection methods, the search process is equivalent to a discrete optimization problem over all possible subsets of summary statistics. In the ellipse search method, we extend the discrete optimization problem to a continuous optimization problem over a compact set of elliptical regions in the space of summary statistics. The method of gradient descent is applied to this new continuous optimization problem. The ellipse search method improves the accuracy of the results of approximate Bayesian computation in addition to improving the speed of computation. |
