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

2019/01/24 by Masayo Y. Hirose, Hirose, Masayo Y., Partha Lahiri +1
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1901.08245

openalex publication_date 2019/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The two-level normal hierarchical model has played an important role in statistical theory and applications. In this paper, 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.

Related

• Selection of inverse gamma and half-t priors for hierarchical models: sensitivity and recommendations
• The R2D2 Prior for Generalized Linear Mixed Models
• A hierarchical prior for generalized linear models based on predictions for the mean response
• Flexible linear mixed models with improper priors for longitudinal and survival data
• On the propriety of the posterior of hierarchical linear mixed models with flexible random effects distributions