Estimation & Prediction

Monte Carlo sampling to approximate prediction error variances and reliabilities in multiple-trait genomic models

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Abstract

Genomic prediction models, such as GBLUP, incorporate genomic data to improve the accuracy of genomically estimated breeding values (GEBVs). However, as the number of genotypes increases, computation of the exact GEBVs and their reliabilities becomes computationally infeasible. Iterative solvers, such as the preconditioned conjugate gradient algorithm, can estimate GEBVs without matrix inversion, but they do not directly provide prediction error variances (PEVs) or reliabilities.Our research investigated approximating PEVs and reliabilities in single-trait and multi-trait genomic models using Monte Carlo (MC) methods. These methods avoid matrix inversion by repeatedly sampling breeding values from their assumed distributions and computing GEBVs using iterative solvers.We evaluated four existing MC-based approximation methods. We applied them to multi-trait genomic models, which included multiple random effects. The convergence of the methods was assessed under varying levels of heritability, population size, and MC sample size, by comparing approximated PEVs and reliabilities to their corresponding exact values computed by direct inversion.The correlations between exact and approximated values varied across the MC methods. These differences can be largely explained by differences in sampling variance. All MC methods converged toward the exact PEVs and reliabilities as the number of MC samples increased. Our results suggest that MC-based approximation methods are applicable in large-scale multi-trait genomic models. As the number of genotypes and traits increased, the computing time of the exact method increased rapidly due to the need to invert the coefficient matrix, whereas the approximation method scaled approximately quadratically with the size of the coefficient matrix.

Keywords: 2026

How to Cite:

Heikkilä, A., Strandén, I., Lidauer, M., Nordhausen, K. & Taskinen, S., (2026) “Monte Carlo sampling to approximate prediction error variances and reliabilities in multiple-trait genomic models”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2275058. doi: https://doi.org/10.31274/wcgalp.23421

Rights: 1