Multi-Goal Prior Selection: A Way to Reconcile Bayesian and Classical Approaches for Random Effects Models

Masayo Y. Hirose, Partha Lahiri

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1487-1497
Number of pages11
JournalJournal of the American Statistical Association
Volume116
Issue number535
DOIs
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'Multi-Goal Prior Selection: A Way to Reconcile Bayesian and Classical Approaches for Random Effects Models'. Together they form a unique fingerprint.

Cite this