Use Model Averaging instead of Model Selection in Pulsar Timing

TL;DR

This paper advocates replacing model selection with model averaging using Spike and Slab priors in pulsar timing Bayesian analysis to avoid circular analysis errors and improve gravitational wave detection.

Contribution

It introduces Spike and Slab priors as a novel approach for model averaging, replacing traditional model selection in pulsar timing Bayesian inference.

Findings

Spike and Slab priors are equivalent to Log-Uniform priors.

Model averaging reduces circular analysis errors.

Proposed method improves parameter estimation accuracy.

Abstract

Over the past decade and a half, adoption of Bayesian inference in pulsar timing analysis has led to increasingly sophisticated models. The recent announcement of evidence for a stochastic background of gravitational waves by various pulsar timing array projects highlighted Bayesian inference as a central tool for parameter estimation and model selection. Despite its success, Bayesian inference is occasionally misused in the pulsar timing community. A common workflow is that the data is analyzed in multiple steps: a first analysis of single pulsars individually, and a subsequent analysis of the whole array of pulsars. A mistake that is then sometimes introduced stems from using the posterior distribution to craft the prior for the analysis of the same data in a second step, a practice referred to in the statistics literature as ``circular analysis.'' This is done to prune the model for computational efficiency. Multiple recent high-profile searches for gravitational waves by pulsar timing array (PTA) projects have this workflow. This letter highlights this error and suggests that Spike and Slab priors can be used to carry out model averaging instead of model selection in a single pass. Spike and Slab priors are proved to be equal to Log-Uniform priors.