Restricted Type II Maximum Likelihood Priors on Regression Coefficients
In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to undesirable behavior in testing (see Lindley’s paradox; Lindley (1957)). We study the properties of some restricted type II maximum likelihood (type II ML) priors on regression coefficients. In type II ML, hyperparameters are “ estimated ” by maximizing the marginal likelihood of a model. In this article, we define priors by estimating their variances or covariance matrices, adding restrictions which ensure that the resulting priors are at least as vague as conventional proper priors for model uncertainty. We find that these type II ML priors typically yield results that are close to answers obtained with the Bayesian Information Criterion (BIC; Schwarz (1978)).
Duke Scholars
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Citation
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 0104 Statistics