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Estimation of prediction error variances via Monte Carlo sampling methods using different formulations of the prediction error variance

John M Hickey123*, Roel F Veerkamp1, Mario PL Calus1, Han A Mulder1 and Robin Thompson456

Author Affiliations

1 Animal Breeding and Genomics Centre, Animal Sciences Group, PO Box 65, 8200 AB, Lelystad, The Netherlands

2 Grange Beef Research Centre, Teagasc, Dunsany, Co. Meath, Ireland

3 School of Agriculture, Food and Veterinary Medicine, College of Life Sciences, University College Dublin, Belfield, Dublin 4, Ireland

4 School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK

5 Centre for Mathematical and Computational Biology, Rothamsted Research, Harpenden AL5 2JQ, UK

6 Department of Biomathematics and Bioinformatics, Rothamsted Research, Harpenden AL5 2JQ, UK

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Genetics Selection Evolution 2009, 41:23  doi:10.1186/1297-9686-41-23

Published: 9 February 2009

Abstract

Calculation of the exact prediction error variance covariance matrix is often computationally too demanding, which limits its application in REML algorithms, the calculation of accuracies of estimated breeding values and the control of variance of response to selection. Alternatively Monte Carlo sampling can be used to calculate approximations of the prediction error variance, which converge to the true values if enough samples are used. However, in practical situations the number of samples, which are computationally feasible, is limited. The objective of this study was to compare the convergence rate of different formulations of the prediction error variance calculated using Monte Carlo sampling. Four of these formulations were published, four were corresponding alternative versions, and two were derived as part of this study. The different formulations had different convergence rates and these were shown to depend on the number of samples and on the level of prediction error variance. Four formulations were competitive and these made use of information on either the variance of the estimated breeding value and on the variance of the true breeding value minus the estimated breeding value or on the covariance between the true and estimated breeding values.