Exact prior-free probabilistic inference on the heritability coefficient in a linear mixed model

TL;DR

This paper introduces a new exact, prior-free probabilistic method for inferring the heritability coefficient in linear mixed models, providing precise confidence intervals and improved efficiency over existing techniques.

Contribution

The paper develops an exact inferential model approach for heritability in linear mixed models, offering prior-free probabilistic inference and superior numerical performance.

Findings

Constructs exact confidence intervals for heritability.

Demonstrates numerical efficiency over existing methods.

Provides a prior-free probabilistic inference framework.

Abstract

Linear mixed-effect models with two variance components are often used when variability comes from two sources. In genetics applications, variation in observed traits can be attributed to biological and environmental effects, and the heritability coefficient is a fundamental quantity that measures the proportion of total variability due to the biological effect. We propose a new inferential model approach which yields exact prior-free probabilistic inference on the heritability coefficient. In particular we construct exact confidence intervals and demonstrate numerically our method's efficiency compared to that of existing methods.