Path-integral Evidence

TL;DR

This paper introduces a Bayesian formalism based on path integrals to evaluate the evidence for a fixed model against perturbations, optimizing experimental design in cosmology.

Contribution

It presents a novel Bayesian path-integral approach for model comparison, specifically applied to dark energy perturbations, under Gaussian data assumptions.

Findings

Provides a method to optimize experiments for model evidence detection

Demonstrates the formalism with a cosmological dark energy example

Offers a new tool for Bayesian model assessment in physics

Abstract

Here we present a Bayesian formalism for the goodness-of-fit that is the evidence for a fixed functional form over the evidence for all functions that are a general perturbation about this form. This is done under the assumption that the statistical properties of the data can be modelled by a multivariate Gaussian distribution. We use this to show how one can optimise an experiment to find evidence for a fixed function over perturbations about this function. We apply this formalism to an illustrative problem of measuring perturbations in the dark energy equation of state about a cosmological constant.