What is empirical Bayes?
hardAnswer
- Estimate the hyperparameters of the prior from the data itself (usually by marginal maximum likelihood), then use that prior for the posterior.
- Cheap approximation to a full hierarchical Bayesian model — avoids MCMC on hyperpriors.
- Uses: shrinkage for large-scale multiple testing (Efron's LFDR), gene expression, hierarchical rate estimation.
- Weakness: ignores uncertainty in the hyperparameter → slightly narrower posteriors than full Bayes.
Check yourself — multiple choice
- Random
- Estimate hyperparameters from data via marginal MLE, then use prior; cheap approximation to hierarchical Bayes; ignores hyperparameter uncertainty
- Same as MAP
- Not real
Empirical Bayes: hyperparameters from data via marginal MLE; cheap hierarchical approx.
#bayesian#estimation
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