Estimation & Prediction

Augmented Monte Carlo Average Information REML: An algorithm to scale up (co)variance component estimation

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Abstract

The aim of this study was to investigate the computational and statistical benefits of applying an augmented Monte Carlo (MC) average information REML (AI-REML) algorithm for (co)variance component (VC) estimation in genomic models. Genomic selection programs require VC estimation, but dense genomic data make inversion of the large coefficient matrix of mixed model equations (MME) computationally infeasible, limiting the use of analytical REML methods in large datasets. MC Expectation Maximization (EM)-REML has been proposed to avoid matrix inversion, but the algorithm has a slow convergence characteristic. The widely used standard AI-REML algorithm, in contrast, offers fast convergence for VC estimation. However, when large genomic models are solved by iterative approaches, MC AI-REML becomes inefficient, because it requires solving the MME separately for each VC parameter. In this study, we implemented an augmented MC AI-REML algorithm that overcomes this bottleneck by solving an augmented MME only once per REML iteration. This approach preserves the theoretical accuracy and Newton-type convergence properties of standard MC AI-REML while substantially reducing computational workload within each REML round. The augmented MC AI-REML uses MC samples generated from the same distribution as the original model to approximate prediction error (co)variances (PEV). This approach leverages preconditioned conjugate gradients (PCG) and iteration-on-data (IOD) techniques in solving the MME, to avoid explicit factorization or inversion of the MME and enable on-the-fly computations suitable for large-scale analyses. We applied the approach for multi-trait GBLUP and SNPBLUP models and evaluated it on real genomic datasets, benchmarking against analytical AI-REML and MC EM-REML. Overall, the augmented MC AI-REML produced identical VC estimates within numerical tolerance compared to those obtained with analytical AI-REML and MC EM-REML for both the multi-trait GBLUP and SNPBLUP models. As expected, augmented MC AI-REML retained Newton-type convergence and converged in fewer iterations than MC EM-REML. These results indicate that the augmented MC AI-REML provides a tractable and scalable solution for multi-trait VC estimation in genomic evaluation, supporting high-throughput prediction pipelines in both animal and plant breeding programs.

Keywords: 2026

How to Cite:

Gao, H., Lidauer, M., Mäntysaari, E., Strandén, I. & Thompson, R., (2026) “Augmented Monte Carlo Average Information REML: An algorithm to scale up (co)variance component estimation”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2286435. doi: https://doi.org/10.31274/wcgalp.24005

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