Detecting episodes of star formation using Bayesian model selection

Abstract

ABSTRACT Bayesian model comparison frameworks can be used when fitting models to data in order to infer the appropriate model complexity in a data-driven manner. We aim to use them to detect the correct number of major episodes of star formation from the analysis of the spectral energy distributions (SEDs) of galaxies, modelled after 3D-HST galaxies at z ∼ 1. Starting from the published stellar population properties of these galaxies, we use kernel density estimates to build multivariate input parameter distributions to obtain realistic simulations. We create simulated sets of spectra of varying degrees of complexity (identified by the number of parameters), and derive SED fitting results and pieces of evidence for pairs of nested models, including the correct model as well as more simplistic ones, using the bagpipes codebase with nested sampling algorithm multinest. We then ask the question: is it true – as expected in Bayesian model comparison frameworks – that the correct model has larger evidence? Our results indicate that the ratio of pieces of evidence (the Bayes factor) is able to identify the correct underlying model in the vast majority of cases. The quality of the results improves primarily as a function of the total S/N in the SED. We also compare the Bayes factors obtained using the evidence to those obtained via the Savage–Dickey density ratio (SDDR), an analytic approximation that can be calculated using samples from regular Markov Chain Monte Carlo methods. We show that the SDDR ratio can satisfactorily replace a full evidence calculation provided that the sampling density is sufficient.