Limitations of Bayesian Evidence Applied to Cosmology

TL;DR

This paper critiques the use of Bayesian Evidence in cosmology, highlighting its limitations and advocating for Bayesian parameter estimation as a more reliable approach in certain model comparisons.

Contribution

It demonstrates the limitations of Bayesian Evidence in cosmological model selection and suggests Bayesian parameter estimation as a more effective alternative.

Findings

Bayesian Evidence shows insignificant preference for cosmological constant.

Subjective choices in priors affect Bayesian Evidence outcomes.

Bayesian parameter estimation can be more informative for nested models.

Abstract

There has been increasing interest by cosmologists in applying Bayesian techniques, such as Bayesian Evidence, for model selection. A typical example is in assessing whether observational data favour a cosmological constant over evolving dark energy. In this paper, the example of dark energy is used to illustrate limitations in the application of Bayesian Evidence associated with subjective judgements concerning the choice of model and priors. An analysis of recent cosmological data shows a statistically insignificant preference for a cosmological constant over simple dynamical models of dark energy. It is argued that for nested problems, as considered here, Bayesian parameter estimation can be more informative than computing Bayesian Evidence for poorly motivated physical models.