The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
Inference with normal-gamma prior distributions in regression problems
Open accessAbstract
This paper considers the effects of placing an absolutely continuous prior distribution on the regression coefficients of a linear model. We show that the posterior expectation is a matrix-shrunken version of the least squares estimate where the shrinkage matrix depends on the derivatives of the prior predictive density of the least squares estimate. The special case of the normal-gamma prior, which generalizes the Bayesian Lasso (Park and Casella 2008), is studied in depth. We discuss the prior interpretation and the posterior effects of hyperparameter choice and suggest a data-dependent default prior. Simulations and a chemometric example are used to compare the performance of the normal-gamma and the Bayesian Lasso in terms of out-of-sample predictive performance.
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Cites
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Cited by
Polygenic prediction via Bayesian regression and continuous shrinkage priors
Ge, T., Chen, C.-Y., Ni, Y., Feng, Y.-C. A., & Smoller, J. W. (2019) · Nature Communications · doi:10.1038/s41467-019-09718-5 · Cited by 1,922
Bayesian linear regression with sparse priors
Castillo, I., Schmidt-Hieber, J., & van der Vaart, A. (2015) · The Annals of Statistics · doi:10.1214/15-aos1334 · Cited by 277
Variational Bayesian inference for linear and logistic regression
Drugowitsch, J. (2013) · arXiv · doi:10.48550/arxiv.1310.5438 · Cited by 49
Metadata
- Authors
- Brown, P. J., & Griffin, J. E.
- Venue
- Bayesian Analysis
- Publisher
- Institute of Mathematical Statistics
- Published
- 2010-03-01
- Volume
- 5
- Issue
- 1
- Pages
- 171-188
- ISSN
- 1931-6690 (ISSN-L)
- 1936-0975
- OpenAlex
- W1966411627
- Cited by
- 462
- References
- 22
- FWCI
- 20.20
- Type
- journal article
- Language
- en
- Open access
- diamond
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