A Bayesian inference and model selection algorithm with an optimisation scheme to infer the model noise power

TL;DR

This paper introduces an adaptive importance sampling algorithm, ATAIS, for Bayesian inference that automatically estimates noise power and efficiently compares models, demonstrated on simulated and real Kepler data.

Contribution

The paper presents a novel adaptive importance sampling method that automatically estimates noise variance and improves model comparison efficiency in Bayesian inference.

Findings

ATAIS accurately estimates noise power in models.

It enables direct computation of model evidence from importance weights.

The method reduces computational time through parallelisation.

Abstract

Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent years, Bayesian inference tools have gained traction. Usually, Markov chain Monte Carlo methods are applied to inference problems, but they present some disadvantages, particularly when comparing different models fitted to the same dataset. Other Bayesian methods can deal with this issue in a natural and effective way. We have implemented an importance sampling algorithm adapted to Bayesian inference problems in which the power of the noise in the observations is not known a priori. The main advantage of importance sampling is that the model evidence can be derived directly from the so-called importance weights -- while MCMC methods demand considerable postprocessing. The use of our adaptive target, adaptive importance sampling (ATAIS) method is shown by inferring, on the one hand, the parameters of a simulated flaring event which includes a damped oscillation {and, on the other hand, real data from the Kepler mission. ATAIS includes a novel automatic adaptation of the target distribution. It automatically estimates the variance of the noise in the model. ATAIS admits parallelisation, which decreases the computational run-times notably. We compare our method against a nested sampling method within a model selection problem.