In many inference problems, the evaluation of complex and costly models is
often required. In this context, Bayesian methods have become very popular in
several fields over the last years, in order to obtain parameter inversion,
model selection or uncertainty quantification. Bayesian inference requires the
approximation of complicated integrals involving (often costly) posterior
distributions. Generally, this approximation is obtained by means of Monte
Carlo (MC) methods. In order to reduce the computational cost of the
corresponding technique, surrogate models (also called emulators) are often
employed. Another alternative approach is the so-called Approximate Bayesian
Computation (ABC) scheme. ABC does not require the evaluation of the costly
model but the ability to simulate artificial data according to that model.
Moreover, in ABC, the choice of a suitable distance between real and artificial
data is also required. In this work, we introduce a novel approach where the
expensive model is evaluated only in some well-chosen samples. The selection of
these nodes is based on the so-called compressed Monte Carlo (CMC) scheme. We
provide theoretical results supporting the novel algorithms and give empirical
evidence of the performance of the proposed method in several numerical
experiments. Two of them are real-world applications in astronomy and satellite
remote sensing.Comment: published in IEEE Transactions on Aerospace and Electronic System