Compressed particle methods for expensive models with application in Astronomy and Remote Sensing

TL;DR

This paper introduces a novel compressed Monte Carlo approach that reduces the computational cost of Bayesian inference for expensive models, demonstrated through applications in astronomy and remote sensing.

Contribution

The paper proposes a new method combining compressed Monte Carlo with Bayesian inference to efficiently evaluate costly models, supported by theoretical analysis and empirical experiments.

Findings

Significant reduction in computational cost compared to traditional methods

Effective application to real-world astronomy and remote sensing problems

Theoretical guarantees for the proposed algorithms

Abstract

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.