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An invariant form for the prior probability in estimation problems
Abstract
It is shown that a certain differential form depending on the values of the parameters in a law of chance is invariant for all transformations of the parameters when the law is differentiable with regard to all parameters. For laws containing a location and a scale parameter a form with a somewhat restricted type of invariance is found even when the law is not everywhere differentiable with regard to the parameters. This form has the properties required to give a general rule for stating the prior probability in a large class of estimation problems.
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Citations
Cited by
Bias reduction of maximum likelihood estimates
FIRTH, D. (1993) · Biometrika · doi:10.1093/biomet/80.1.27 · Cited by 5,035
(2003) · Cited by 1,680
Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods
Hüllermeier, E., & Waegeman, W. (2021) · Machine Learning · doi:10.1007/s10994-021-05946-3 · Cited by 1,834
“See work on “non-informative” priors, however (Jeffreys, 1946; Bernardo, 1979). dominated probability distributions: P ..= { P ∈ P”
BackgroundMathematical Foundations of Information Theory.
Snell, J. L., Khinchin, A. I., Silverman, R. A., & Friedman, M. D. (1959) · The American Mathematical Monthly · doi:10.2307/2310044 · Cited by 1,451
The Selection of Prior Distributions by Formal Rules
Kass, R. E., & Wasserman, L. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10477003 · Cited by 1,308
Metadata
- Authors
- Jeffreys, H.
- Venue
- Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1946-09-24
- Volume
- 186
- Issue
- 1007
- Pages
- 453-461
- ISSN
- 0080-4630 (ISSN-L)
- 2053-9169
- OpenAlex
- W2006681603
- Cited by
- 2,323
- References
- 0
- FWCI
- 1.50
- Type
- journal article
- Language
- en
- Open access
- closed
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- Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. https://doi.org/10.1098/rspa.1946.0056
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