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Conjugate Priors for Exponential Families
Open accessAbstract
Let $X$ be a random vector distributed according to an exponential family with natural parameter $\theta \in \Theta$. We characterize conjugate prior measures on $\Theta$ through the property of linear posterior expectation of the mean parameter of $X : E\{E(X|\theta)|X = x\} = ax + b$. We also delineate which hyperparameters permit such conjugate priors to be proper.
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Cites
Stein's Estimation Rule and its Competitors—An Empirical Bayes Approach
Efron, B., & Morris, C. (1973) · Journal of the American Statistical Association · doi:10.1080/01621459.1973.10481350 · Cited by 981
Cited by
The trouble with overconfidence.
Moore, D. A., & Healy, P. J. (2008) · Psychological Review · doi:10.1037/0033-295x.115.2.502 · Cited by 2,358
Group representations in probability and statistics
Diaconis, P. (1988) · doi:10.1214/lnms/1215467407 · Cited by 1,381
Self-citationOn the Consistency of Bayes Estimates
Diaconis, P., & Freedman, D. (1986) · The Annals of Statistics · doi:10.1214/aos/1176349830 · Cited by 608
Self-citationDealing with uncertainty in model updating for damage assessment: a review
Simoen, E., De Roeck, G., & Lombaert, G. (2015) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2014.11.001 · Cited by 540
Automatic differentiation variational inference
Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A., & Blei, D. M. (2016) · arXiv · doi:10.48550/arxiv.1603.00788 · Cited by 515
Metadata
- Authors
- Diaconis, P., & Ylvisaker, D.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1979-03-01
- Volume
- 7
- Issue
- 2
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2143143555
- Cited by
- 700
- References
- 1
- FWCI
- 7.60
- Type
- journal article
- Language
- en
- Open access
- bronze
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