BAMBI: blind accelerated multimodal Bayesian inference
  In this paper we present an algorithm for rapid Bayesian analysis that
combines the benefits of nested sampling and artificial neural networks. The
blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements
the MultiNest package for nested sampling as well as the training of an
artificial neural network (NN) to learn the likelihood function. In the case of
computationally expensive likelihoods, this allows the substitution of a much
more rapid approximation in order to increase significantly the speed of the
analysis. We begin by demonstrating, with a few toy examples, the ability of a
NN to learn complicated likelihood surfaces. BAMBI's ability to decrease
running time for Bayesian inference is then demonstrated in the context of
estimating cosmological parameters from Wilkinson Microwave Anisotropy Probe
and other observations. We show that valuable speed increases are achieved in
addition to obtaining NNs trained on the likelihood functions for the different
model and data combinations. These NNs can then be used for an even faster
follow-up analysis using the same likelihood and different priors. This is a
fully general algorithm that can be applied, without any pre-processing, to
other problems with computationally expensive likelihood functions.
