2,413 research outputs found
GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation
Scientists often express their understanding of the world through a
computationally demanding simulation program. Analyzing the posterior
distribution of the parameters given observations (the inverse problem) can be
extremely challenging. The Approximate Bayesian Computation (ABC) framework is
the standard statistical tool to handle these likelihood free problems, but
they require a very large number of simulations. In this work we develop two
new ABC sampling algorithms that significantly reduce the number of simulations
necessary for posterior inference. Both algorithms use confidence estimates for
the accept probability in the Metropolis Hastings step to adaptively choose the
number of necessary simulations. Our GPS-ABC algorithm stores the information
obtained from every simulation in a Gaussian process which acts as a surrogate
function for the simulated statistics. Experiments on a challenging realistic
biological problem illustrate the potential of these algorithms
Bayesian optimisation for likelihood-free cosmological inference
Many cosmological models have only a finite number of parameters of interest,
but a very expensive data-generating process and an intractable likelihood
function. We address the problem of performing likelihood-free Bayesian
inference from such black-box simulation-based models, under the constraint of
a very limited simulation budget (typically a few thousand). To do so, we adopt
an approach based on the likelihood of an alternative parametric model.
Conventional approaches to approximate Bayesian computation such as
likelihood-free rejection sampling are impractical for the considered problem,
due to the lack of knowledge about how the parameters affect the discrepancy
between observed and simulated data. As a response, we make use of a strategy
previously developed in the machine learning literature (Bayesian optimisation
for likelihood-free inference, BOLFI), which combines Gaussian process
regression of the discrepancy to build a surrogate surface with Bayesian
optimisation to actively acquire training data. We extend the method by
deriving an acquisition function tailored for the purpose of minimising the
expected uncertainty in the approximate posterior density, in the parametric
approach. The resulting algorithm is applied to the problems of summarising
Gaussian signals and inferring cosmological parameters from the Joint
Lightcurve Analysis supernovae data. We show that the number of required
simulations is reduced by several orders of magnitude, and that the proposed
acquisition function produces more accurate posterior approximations, as
compared to common strategies.Comment: 16+9 pages, 12 figures. Matches PRD published version after minor
modification
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