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.