Generalisations of Fisher Matrices

TL;DR

This paper reviews recent extensions of Fisher matrix methods, including handling errors in data, systematic errors, higher-order likelihood approximations, and Bayesian model selection, enhancing their applicability in experimental design and data analysis.

Contribution

It introduces and discusses several recent developments that extend Fisher matrix formalism to more complex and realistic data analysis scenarios.

Findings

Extended Fisher matrices for data with errors in both variables.

Inclusion of systematic errors and parameter fixing in Fisher analysis.

Development of DALI for higher-order likelihood approximations.

Abstract

Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters - both their errors and covariances. In this short review, I outline a number of extensions to the simple Fisher matrix formalism, covering a number of recent developments in the field. These are: (a) situations where the data (in the form of (x,y) pairs) have errors in both x and y; (b) modifications to parameter inference in the presence of systematic errors, or through fixing the values of some model parameters; (c) Derivative Approximation for LIkelihoods (DALI) - higher-order expansions of the likelihood surface, going beyond the Gaussian shape approximation; (d) extensions of the Fisher-like formalism, to treat model selection problems with Bayesian evidence.