Simple and statistically sound recommendations for analysing physical theories

TL;DR

This paper provides physicists with straightforward, statistically sound methods and practical guidance for analyzing complex physical theories involving many parameters, addressing common pitfalls of ad hoc approaches.

Contribution

It introduces clear, simple statistical inference techniques and recommends accessible software tools to improve analysis accuracy in physical sciences.

Findings

Identifies issues with traditional ad hoc methods in high-dimensional spaces.

Proposes statistically rigorous alternatives for parameter estimation.

Provides reproducible examples and software resources.

Abstract

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at https://doi.org/10.5281/zenodo.4322283.