Generalisations of Fisher Matrices

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.

Invited review article for Entropy special issue on 'Applications of Fisher Information in Sciences'. Accepted version

References in corpus (5)

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• A Fresh Approach to Forecasting in Astroparticle Physics and Dark Matter Searches
• Cosmology with Galaxy Cluster Phase Spaces
• Impact of Galactic dust non-Gaussianity on searches for B-modes from inflation
• Cosmological studies from tomographic weak lensing peak abundances and impacts of photo-z errors
• Beyond Fisher Forecasting for Cosmology