Generalisations of Fisher Matrices
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, coverin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-06-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/18/6/236 |
| _version_ | 1798040240435232768 |
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| author | Alan Heavens |
| author_facet | Alan Heavens |
| author_sort | Alan Heavens |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:04:44Z |
| format | Article |
| id | doaj.art-07b3ad44b5f8419aac0d88b5c2e4feda |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:04:44Z |
| publishDate | 2016-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-07b3ad44b5f8419aac0d88b5c2e4feda2022-12-22T04:00:46ZengMDPI AGEntropy1099-43002016-06-0118623610.3390/e18060236e18060236Generalisations of Fisher MatricesAlan Heavens0Imperial Centre for Inference and Cosmology (ICIC), Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UKFisher 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.http://www.mdpi.com/1099-4300/18/6/236fisher matricesstatisticsexperimental design |
| spellingShingle | Alan Heavens Generalisations of Fisher Matrices Entropy fisher matrices statistics experimental design |
| title | Generalisations of Fisher Matrices |
| title_full | Generalisations of Fisher Matrices |
| title_fullStr | Generalisations of Fisher Matrices |
| title_full_unstemmed | Generalisations of Fisher Matrices |
| title_short | Generalisations of Fisher Matrices |
| title_sort | generalisations of fisher matrices |
| topic | fisher matrices statistics experimental design |
| url | http://www.mdpi.com/1099-4300/18/6/236 |
| work_keys_str_mv | AT alanheavens generalisationsoffishermatrices |