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O Uso da Estatística Bayesiana no Melhoramento Genético Animal: Uma Breve Explicação

DOI: http://dx.doi.org/10.18188/1983-1471/sap.v12n4p247-257

http://e-revista.unioeste.br/index.php/scientiaagraria/index 

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Marcos J. I. Yokoo1, Guilherme J. de M. Rosa2, Fernando F. Cardoso1, Cláudio de U. Magnabosco3 & Lucia G. Albuquerque4

 

Resumo: Este trabalho aborda o estudo de técnicas bayesianas no melhoramento genético animal, no intuito de discutir e elucidar essa abordagem frente à “estatística frequentista”. Apresentam-se dois algoritmos de integração estocástica por meio da simulação de Monte Carlo em Cadeias de Markov (MCMC): o Amostrador de Gibbs e o Metropolis-Hastings. Considera-se a aplicação das mencionadas técnicas como uma alternativa aos programas de melhoramento animal, na estimação de parâmetros genéticos em ordem de solucionar problemas relacionados aos modelos mais complexos e a expressão de características de interesse econômico que não tenham distribuição normal. Assim, alternativas bayesianas constituem uma excelente estratégia para contornar essas situações, por meio de modelos com outras distribuições, além da normal, tendo mostrado eficiência e fácil implementação para estimação confiável de parâmetros. Além disso, a inferência bayesiana tem a vantagem adicional de permitir a incorporação de informações passadas (a priori), melhorando o processo de estimação. As abordagens propostas são explicadas e discutidas no desenvolvimento do trabalho.

Palavras-chaves: amostrador de Gibbs; método de MCMC; Metropolis-Hastings; parâmetro; verossimilhança.

 

Abstract: This paper describes the study of Bayesian techniques in animal breeding, aiming to discuss and clarify this approach compared to “frequentist statistics”. We present two algorithms for stochastic integration by using Markov Chain Monte Carlo (MCMC) simulation: Gibbs sampling and Metropolis-Hastings algorithm. The application of these techniques is considered an alternative to animal breeding programs in the estimation of genetic parameters to solve problems related to more complex models and the expression of traits of economic interest that do not have normal distribution. Therefore, Bayesian techniques become an excellent strategy to elucidate these situations, by using models with alternative distributions, which have shown efficiency and easy implementation for reliable estimation of parameters. Furthermore, Bayesian inference has the additional advantage of allowing the incorporation of previous (a priori) information, improving the estimation process. The proposed approaches are explained and discussed in the development of this paper.

Key words  : Gibbs sampler; likelihood; MCMC method; Metropolis-Hastings; parameter; verisimilitude.

 

1 Empresa Brasileira de Pesquisa Agropecuária, Centro de Pesquisa de Pecuária dos Campos Sul-Brasileiros - Embrapa Pecuária Sul - CPPSul, BR 153, km 603, Caixa Postal 242, CEP 96401-970, Bagé/RS, Brasil. E-mail: marcos.yokoo@embrapa.br. *Autor para correspondência
2 Department of Animal Science, University of Wisconsin, Madison, WI 53706, USA.
3 Empresa Brasileira de Pesquisa Agropecuária, Embrapa Cerrados - CNPAF, BR 020, km 18, Caixa Postal 08223, CEP 73310-970, Planaltina/DF, Brasil.
4 Universidade Estadual Paulista - UNESP, Faculdade de Ciências Agrárias e Veterinárias, Departamento de Zootecnia, Jaboticabal/SP, Brasil. E-mail: lgalb@fcav.unesp.br

 

Literatura Citada

BERNARDO, J.M.; SMITH, A.F.M. Bayesian theory. John Wiley & Sons, Chichester, U.K. 1994.

BESAG, J.; GREEN, P.; HIGDON, D.; MENGERSEN, K. Bayesian computation and stochastic systems. Statistical Science, v.10, n.1, p.03-66, 1995.

BLASCO, A.The Bayesian controversy in animal breeding. Journal of Animal Science, v.79, p.2023-2046. 2001.

BOX, G.E.P.; TIAO, G.C. Bayesian Inference in Statistical Analysis. New York: J. WileyInterscience, 1992. 588p.

CASELLA, G.; GEORGE, E.I. Explaining the Gibbs Sampler. The American Statistician, v.46, n.3, p.167-174, 1992.

CHIB, S.; GREENBERG, E. Understanding the Metropolis-Hastings Algorithm. The American Statistician, v.49, n.4, p.327-335, 1995.

DEMPFLE, L. Relation entre BLUP (Best Linear Unbiased Prediction) et estimateurs bayesiens. Genetic, Selection, Evolution, v.9, p.27-32, 1977.

DUCROQ, V.; CASELLA, G.A. Bayesian analysis of mixed survival models. Genetic, Selection, Evolution, v.28, p.505-529, 1996.

FORNI, S.; PILES, M.; BLASCO, A.; VARONA L.; OLIVEIRA, H.N.; LÔBO, R.B.; ALBUQUERQUE, L.G. Comparison of different nonlinear functions to describe Nelore cattle growth. Journal of Animal Science, v.87, p.496-506, 2009.

GELFAND, A.E.; SMITH, A.F.M. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, v.85, n.410, p.348-409, 1990.

GELFAND, A.E. Gibbs sampling. Journal of the American Statistical Association, v.95, n.452, p.1300-1304, 2000.

GELFAND, A.E.; HILLS, S.E.; RACINE-POON, A.; SMITH, A.F.M. Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association, v.85, n.41, p.972-985, 1990.

GELMAN, A.; RUBIN, D.B. Inference from iterative simulation using multiple sequence. Statistical Science, Hayward, v.7, n.4, p.457-511, 1992.

GEMAN, S.; GEMAN. D. Stochastic relaxation, Gibbs distribution and Bayesian restoration of images. IEE Transactions on Pattern Analysis and Machine Intelligence, v.6, p.721–741, 1984.

GEYER, C.J. Practical Markov chain Monte Carlo (with discussion). Statistical Science, v.7, p.473-511, 1992.

GIANOLA, D.; FERNANDO, R.L. Bayesian methods in animal breeding theory. Journal of Animal Science, v.63, p.217-244, 1986.

GIANOLA, D.; FOLLEY, J.L. Non linear prediction of latent genetic liability with binary expression: An empirical Bayes approach. In: WORLD CONGRESS OF GENETIC APPLIED TO LIVESTOCK PRODUCTION, 2., Madri, Espanha, 1982. Proceedings…Madri, v.7, p.293303. 1982.

GOMPERT, Z.; BUERKLE, C.A.A Hierarchical Bayesian Model for Next-Generation Population Genomics. Genetics, v.187, p.903-917, 2011.

GREEN, P.J. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, v.82, n.4, p. 711-732, 1995.

HARTLEY, H.O.; RAO, J.N.K. Maximum likelihood estimation for the mixed analysis of variance model. Biometrika, v.54, p.93-108, 1967.

HARVILLE, D.A. Bayesian inferences for variance components using only error contrasts. Biometrika, v.61, p.383-385, 1974.

HASTINGS, W.K. Monte Carlo sampling methods using Markov Chains and their applications. Biometrika, v.57, p.97-109, 1970.

HENDERSON, C.R. Estimation of variance and covariance components. Biometrics, v.17, p.226-252, 1953.

HENDERSON, C.R. Sire evaluation and genetic trends. In: ANIMAL BREEDING AND GENETIC SYMPOSIUM IN HONOR OF DR. JAY L. LUSH, 1., Champaign, IL, EUA, 1973. Proceedings… Champaign, IL: ASAS, p.10-41. 1973.

JAMROZIK, J.; SCHAEFFER, L.R. Estimates of genetic parameters for a test day model with random regressions for yield of first lactation Holsteins. Journal of Dairy Science, v.80, p.72670, 1997.

METROPOLIS, N.; ROSENBLUTH, A.W.; ROSENBLUTH, M.N.; TELLER, A.; TELLER, H. Equations of state calculations by fast computing machines. Journal of Chemical Physics, v.21, p.1087-1091, 1953.

MEUWISSEN, T.H.E.; GODDARD, M.E.; HAYES, B.J. Prediction of total genetic value using genome-wide dense marker maps. Genetics, v.157, p.1819-1829, 2001.

MIGNON-GRASTEAU, S.; PILES, M.; VARONA, L.; ROCHAMBEAU, H.; POIVEY, J.P.; BLASCO, A.; BEAUMONT, C. Genetic analysis of growth curve parameters for male and female chickens resulting from selection based on juvenile and adult body weights simultaneously. Journal of Animal Science, v.78, p.2515-2524, 2000.

PATTERSON, H.D.; THOMPSON, R. Recovery of inter-block information when block size are unequal. Biometrics, v.58, p.545-554. 1971.

RAFTERY, A.E.; LEWIS, S.M. Comment: One long run with diagnostics: Implementation strategies for Markov Chain Monte Carlo. Statistical Science, v.7, p.493-497, 1992.

RAO, C.R. Estimation of variance and covariance components – MINQUE theory. Journal of Multivariate Analysis, v.1, p.257-275, 1971a.

RAO, C.R. Minimum variance quadratic unbiased estimation of variance components. Journal of Multivariate Analysis, v.1, p.445-456, 1971b.

RONNINGEN, K. Some properties of the selection index derived by “Henderson’s mixed model method”. ZeitschriftfürTierzüchtung und Züchtungsbiologie, v.88, p.186-193, 1971.

ROSA, G.J.M.; YANDELL, B.S.; GIANOLA, D.A Bayesian approach for constructing genetic maps when markers are miscoded. Genetic, Selection, Evolution, v.34, p.353-369, 2002.

SATAGOPAN, J.M.; YANDELL, B.S.; NEWTON, M.A.; OSBORN, T.C.A Bayesian approach to detect quantitative trait loci using Markov Chain Monte Carlo. Genetics, v.144, p.805-816, 1996.

SCHENKEL, F.S.; SCHAEFFER, L.R.; BOETTCHER, P.J. Comparison between estimation of breeding values and fixed effects using Bayesian and empirical BLUP estimation under selection on parents and missing pedigree information. Genetic, Selection, Evolution, v.34, p.41-59, 2002.

SEARLE, S.R. Linear models for unbalanced data. New York: John Wiley & Sons, 1987. 536p.

STIGLER, S.M. The History of Statistics: The Measurement of Uncertainty before 1900. Harvard University Press, Cambridge, MA. 1986.

STIGLER, S.M. Who discovered Bayes’s theorem? American Statistician, v.37, p.290-296, 1983.

TANNER, M.A. Tools for statistical inference, 3ed. Springer-Verlag, New York. 1996.

TEMPELMAN, R.J. Generalized Linear Mixed Models in Dairy Cattle Breeding. Journal of Dairy Science, v.81, p.1428-1444, 1998.

TIERNEY, L. Markov chains for exploring posterior distributions. The Annals of Statistics, v.22, p.1701-1762, 1994.

UIMARI, P.; HOESCHELE, I. Mapping-linked quantitative trait loci using Bayesian analysis and Markov Chain Monte Carlo algorithms. Genetics, v.146, p.735-743, 1997.

VAN TASSEL, C.P.; CASELLA, G.; POLLAK, E.J. Effects of selection on estimates of variance components using Gibbs sampling and restricted maximum likelihood. Journal of Dairy Science, v.78, p.678-692, 1995.

VARONA, L., MORENO, C., GARCIA-CORTE´S, L.A., ALTARRIBA, J. Multiple trait genetic analysis of underlying biological variables of production functions. Livestock Production Science, v.47, p.201-209, 1997.

WANG, C.S.; GIANOLA, D.; SORENSEN, D.A.; JENSEN, J.; CHRSTENSEN, A.; RUTHLETDGE, J.J. Response to Selection for Letter Size in Danish Landrace Pigs: A Bayesian Analysis. Theory Applied Genetics, v.88, p.220-230, 1994.