Fisher Matrices and Confidence Ellipses: A Quick-Start Guide and Software

TL;DR

This paper provides a clear, concise guide and Python software for using Fisher matrices in cosmological data analysis, covering confidence ellipses, dataset combination, priors, marginalization, and transformations.

Contribution

It offers an accessible, practical reference for applying Fisher matrices in cosmology, including software tools and detailed procedures.

Findings

Easy-to-follow methods for Fisher matrix analysis

Python software implementation provided

Guidance on combining datasets and applying priors

Abstract

Fisher matrices are used frequently in the analysis of combining cosmological constraints from various data sets. They encode the Gaussian uncertainties of multiple variables. They are simple to use, and I show how to get up and running with them quickly. Python software is also provided. I cover how to obtain confidence ellipses, add datasets, apply priors, marginalize, transform variables, and even calculate your own Fisher matrices. This treatment is not new, but I aim to provide a clear and concise reference guide. I also provide references and links to more sophisticated treatments and software.