Empirical Bayes When Estimation Precision Predicts Parameters

Understand

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates.

• This assumption is often theoretically questionable and empirically rejected.
• This paper proposes to model the conditional distribution of the parameter given the standard errors as a flexibly parametrized location-scale family of distributions, leading to a family of methods that we call CLOSE.
• The CLOSE framework unifies and generalizes several proposals under precision dependence.