On the Evidence for Cosmic Variation of the Fine Structure Constant (II): A Semi-Parametric Bayesian Model Selection Analysis of the Quasar Dataset

TL;DR

This paper extends Bayesian analysis of quasar data to semi-parametric models using Dirichlet process priors, improving robustness and reducing subjectivity in testing for variations in the fine structure constant across the universe.

Contribution

It introduces a semi-parametric Bayesian model with Dirichlet process priors for error modeling, enabling more flexible and robust model selection in cosmological data analysis.

Findings

Demonstrates recursive marginal likelihood estimation with sensitivity analysis

Shows similarities between error modeling in astronomy and clinical meta-analysis

Provides a novel semi-parametric approach for model selection in error-prone data

Abstract

In the second paper of this series we extend our Bayesian reanalysis of the evidence for a cosmic variation of the fine structure constant to the semi-parametric modelling regime. By adopting a mixture of Dirichlet processes prior for the unexplained errors in each instrumental subgroup of the benchmark quasar dataset we go some way towards freeing our model selection procedure from the apparent subjectivity of a fixed distributional form. Despite the infinite-dimensional domain of the error hierarchy so constructed we are able to demonstrate a recursive scheme for marginal likelihood estimation with prior-sensitivity analysis directly analogous to that presented in Paper I, thereby allowing the robustness of our posterior Bayes factors to hyper-parameter choice and model specification to be readily verified. In the course of this work we elucidate various similarities between unexplained error problems in the seemingly disparate fields of astronomy and clinical meta-analysis, and we highlight a number of sophisticated techniques for handling such problems made available by past research in the latter. It is our hope that the novel approach to semi-parametric model selection demonstrated herein may serve as a useful reference for others exploring this potentially difficult class of error model.