TY - JOUR
T1 - Multi-Goal Prior Selection
T2 - A Way to Reconcile Bayesian and Classical Approaches for Random Effects Models
AU - Hirose, Masayo Y.
AU - Lahiri, Partha
N1 - Funding Information:
We thank Professor Shuhei Mano, anonymous associate editor, and referees for reading an earlier version of the article carefully and offering a number of constructive suggestions, which led to a significant improvement of our article. The first and second authors’ research was partially supported by JSPS KAKENHI grant number 18K12758 and U.S. National Science Foundation grants SES-1534413 and SES-1758808, respectively.
Publisher Copyright:
© 2020 American Statistical Association.
PY - 2021
Y1 - 2021
N2 - Abstract–The two-level normal hierarchical model has played an important role in statistical theory and applications. In this article, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the model and the associated empirical best linear unbiased predictor of the random effects. We then discuss a new idea for selecting prior for the hyperparameters. The prior, called a multi-goal prior, produces Bayesian solutions for hyperparmeters and random effects that match (in the higher order asymptotic sense) the corresponding classical solution in linear mixed model with respect to several properties. Moreover, we establish for the first time an analytical equivalence of the posterior variances under the proposed multi-goal prior and the corresponding parametric bootstrap second-order mean squared error estimates in the context of a random effects model.
AB - Abstract–The two-level normal hierarchical model has played an important role in statistical theory and applications. In this article, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the model and the associated empirical best linear unbiased predictor of the random effects. We then discuss a new idea for selecting prior for the hyperparameters. The prior, called a multi-goal prior, produces Bayesian solutions for hyperparmeters and random effects that match (in the higher order asymptotic sense) the corresponding classical solution in linear mixed model with respect to several properties. Moreover, we establish for the first time an analytical equivalence of the posterior variances under the proposed multi-goal prior and the corresponding parametric bootstrap second-order mean squared error estimates in the context of a random effects model.
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U2 - 10.1080/01621459.2020.1737532
DO - 10.1080/01621459.2020.1737532
M3 - Article
AN - SCOPUS:85082805502
SN - 0162-1459
VL - 116
SP - 1487
EP - 1497
JO - Quarterly Publications of the American Statistical Association
JF - Quarterly Publications of the American Statistical Association
IS - 535
ER -