ELICITATION OF PRIOR DISTRIBUTIONS TO ESTIMATE VARIANCE COMPONENTS

In the Bayesian context, when variance components are modeled in normal hierarchical models, the inverted gamma distribution (IG) is typically used as the prior density for each component. However, the literature indicates that this prior density is highly informative, and thus the Half Cauchy distribution (HC) is recommended. The aim of this study was to evaluate, using simulation (in the context of high-dimensional data such as in the case of genomic selection applications), the suitability of the scaled inverse chi-squared (X-2v,S) distribution, which belongs to the family of scaled inverse gamma distributions, and HC as prior densities for the variance components in the Bayesian Ridge regression model. The evaluation was carried out when the number of observations in the response variable is greater than the number of predictor variables (n > p) as well as in high dimensions (n p, the REML method underestimates the variance of the random effect, whereas in scenarios in which n p) and n