07: Boon of Dimensionality in Bayesian Heritability Estimation

Music City Center 

In the frequentist framework, Jiang et al. (2016) established the asymptotic properties of the restricted maximum likelihood (REML) estimator under misspecified linear mixed models (LMMs), demonstrating the consistency of the REML estimator for heritability. Our study extends these results to the Bayesian paradigm by considering a non-informative prior on the error variance. We derive the Bayesian marginal maximum likelihood estimator (MMLE) for the signal-to-noise ratio (SNR) and analyze its concentration properties.

Our analysis establishes that the Bayesian MMLE exhibits asymptotic consistency properties analogous to those of the REML estimator. Furthermore, we derive non-asymptotic convergence rates for the Bayesian MMLE, elucidating its behavior under model misspecification, particularly in high-dimensional settings. These results have direct implications for variable selection, uncertainty quantification in hierarchical models, and signal detection in complex data structures.

Bayesian estimation

Restricted Maximum Likelihood Estimator (REML)

Model Misspecification

Signal-to-Noise Ratio (SNR)

Marginal Maximum Likelihood Estimator

Asymptotic Consistency 

Biometrics Section