Abstract
Surrogate models such as Gaussian processes (GP) have been proposed to
accelerate approximate Bayesian computation (ABC) when the statistical model of
interest is expensive-to-simulate. In one such promising framework the
discrepancy between simulated and observed data is modelled with a GP which is
further used to form a model-based estimator for the intractable posterior. In
this article we improve this approach in several ways. We develop
batch-sequential Bayesian experimental design strategies to parallellise the
expensive simulations. In earlier work only sequential strategies have been
used. Current surrogate-based ABC methods also do not fully account the
uncertainty due to the limited budget of simulations as they output only a
point estimate of the ABC posterior. We propose a numerical method to fully
quantify the uncertainty in, for example, ABC posterior moments. We also
provide some new analysis on the GP modelling assumptions in the resulting
improved framework called Bayesian ABC and on its connection to Bayesian
quadrature (BQ) and Bayesian optimisation (BO). Experiments with several toy
and real-world simulation models demonstrate advantages of the proposed
techniques.
Users
Please
log in to take part in the discussion (add own reviews or comments).