Bayesian quantile regression with variable selection and applications in plant breeding

Abstract

High‐dimensional data present major challenges in identifying key predictors of phenotypic variation, particularly when response distributions are asymmetric or heavy tailed. Traditional variable selection methods focus on the conditional mean, limiting their utility in scenarios with heterogeneity across quantiles. This study applies a Bayesian Quantile Regression model with Variable Selection (BQRVS), which extends classical quantile regression through a hierarchical Bayesian framework and provides selective shrinkage of coefficients through hierarchical priors, along with full posterior uncertainty estimation for all parameters. The BQRVS model was evaluated on two real datasets. The first involves the detection of quantitative trait loci associated with grain yield in barley, using genomic markers and quantile‐specific modeling to identify predictors associated with the lower and upper regions of the conditional yield distribution. The second case explores the relationship between hyperspectral reflectance data and grain yield for maize using field‐collected data. In both examples, the model was fitted at multiple quantiles , for probability levels θ ∈ {0.1, 0.5, 0.9} using prior distributions that favor sparsity. Results revealed quantile specific relevance of genomic markers and spectral bands, with certain predictors influencing only low or high quantiles of the response. These findings underscore the importance of moving beyond mean‐based approaches, especially in plant breeding and phenotyping contexts characterized by complex or non‐normal response behavior. The BQRVS framework provides a flexible and efficient tool for robust variable selection and prediction in genomic and spectral data analysis, offering new insights into the structure of trait variation across the distribution of interest.