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Generalisations of Fisher Matrices

Imperial Centre for Inference and Cosmology (ICIC), Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK
Academic Editor: Takuya Yamano
Entropy 2016, 18(6), 236; https://doi.org/10.3390/e18060236
Received: 3 May 2016 / Revised: 16 June 2016 / Accepted: 18 June 2016 / Published: 22 June 2016
(This article belongs to the Special Issue Applications of Fisher Information in Sciences)
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. View Full-Text
Keywords: fisher matrices; statistics; experimental design fisher matrices; statistics; experimental design
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Heavens, A. Generalisations of Fisher Matrices. Entropy 2016, 18, 236.

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