Gibbs Sampler Eliminates Approximation Bias

Research shows that high-performance Gibbs Sampling can eliminate approximation bias in NCE computations.

by Kasey Brown, associate editor, Angus Journal®

LINCOLN, Neb. (June 20, 2014) — There is a lot that goes into genetic predictions and their accuracy, yet a California Polytechnic State University–San Luis Obispo (Cal Poly) researcher proposed that a Gibbs Sampler is better than current approximations. Bruce Golden, head of the Dairy Science Department at Cal Poly, presented to the Advancements in Genetic Prediction Committee at the 2014 Beef Improvement Federation (BIF) Annual Meeting and Research Symposium in Lincoln, Neb., June 18-21.

Golden explained research to determine whether a Gibbs Sampler is better than current approximations for calculating the prediction error variance (PEV) used in BIF accuracy computations. What constitutes better? He answered that better means high correlation to inverse diagonal mixed method equation (MME) elements, sufficiently fast on production-size problems and provides more information.

He asked if parallel chains give the same answer as one long chain? He shared research that showed correlations of posterior means for various sampling strategies, including one chain of 20,000; one chain of 100,000; five chains of 4,000; 10 chains of 2,000; 10 chains of 3,000 with 1,000 burn; and five chains of 20,000. The correlations ranged from .987 to 1.000. The answer to whether parrallel chains give the same answer is yes, he clarified.

The second question was whether the Gibbs Sampler could be sufficiently fast on production-size problems. He added that “gaming” computers are affordable computers that have the power needed to compute such large equations. By using different parallel chain lengths to produce 20,000 samples, Golden found that using Gibbs Sampling was sufficiently fast, with even the longest chain of 20,000 being computed in less than 10 minutes.

With a real-world problem in computing an example of the American Simmental Association’s birth weight, weaning weight and milk expected progeny differences (EPDs), the time to compute 10,000 samples from 10 chains at 1,000 samples each was 196 minutes and 14 seconds.

In conclusion, Golden explained, “The Gibbs Sampler resulted in high-quality PEV estimates that converged to the inverse of the MME; multi-core, overclocking and heterogeneous computing helped make implementing Gibbs Sampling for PEV tractable; and parallel chains started with PCG (preconditioned conjugate gradient) solutions provided a performance improvement and the same answers.”

The 2014 BIF Annual Meeting & Research Symposium was hosted by the University of Nebraska–Lincoln, the U.S. Meat Animal Research Center and the Nebraska Cattlemen June 18-21 in Lincoln, Neb. The Angus Journal and LiveAuctions.tv provide comprehensive online coverage of the event at www.BIFconference.com. Visit the Newsroom for summaries, proceedings, PowerPoints and audio of the sessions; and the Awards page for announcements of award winners.

Editor’s Note: This summary was written under contract or by staff of the Angus Journal.Through an agreement with the Beef Improvement Federation, we are encouraging reprinting of the articles to those who will adhere to the reprint guidelines available on this site. Please review those guidelines or contact Shauna Rose Hermel, editor, at 816-383-5270. PowerPoints are posted with permission of the presenter and may not be reproduced in whole or in part without the express permission of the presenter.

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