Bayesian Methods

This page contains a collection of papers that set milestones in using a Bayesian approach in quantitative genetics. This list is by no means complete history of Bayesian analyses.

• K Rønningen. (1971). Some Properties of the Selection Index derived by “Henderson’s Mixed Model Method”. J Anim Breed Genet. 129:474-487.
  Pehaps this is the first attempt to investigate the connection between BLUP/Selection Index and Bayesian Inference.

• DA Harville. (1974). Bayesian inference for variance components using only error contrasts. Biometrika. 61:383-385.
  This paper demonstrated that when flat priors were assigned for fixed effects and variance components, REML is essentially equal to the mode of the marginal posterior density of the variance components in a Bayesian model.

• D Gianola and RL Fernando. (1986). Bayesian methods in animal breeding theory. J. Anim. Sci. 63:217-244. A comprehensive review of Bayesian methods in the pre MCMC era. It offers a Bayesian view of variance component estimation, prediction of genetic values with or without selection, and non-linear models.

• D Gianola and JL Foulley. (1990). Variance estimation from integrated likelihoods (VEIL). Genet Sel Evol. 22:403-417.
  An attempt to perform Bayesian estimation of variance components in the pre MCMC era.

• AE Gelfand and AFM Smith. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association. 85:398-409.
  One of the first application of Gibbs sampling in genetics.

• SW Guo and EA Thompson. (1991). Monte Carlo estimation of variance component models for large complex pedigrees. IMA J Math Appl Med Biol. 8:171-189.
  The first application of Gibbs sampling in quantitative genetics.

• CS Wang et al. (1993). Marginal inferences about variance components in a mixed linear model using Gibbs sampling. Genet Sel Evol. 25:41-62.
  Gibbs sampling was used first in animal breeding along with simulated data sets and a sire model.

• CS Wang et al. (1994). Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs. Genet Sel Evol. 26:91-115.
  The first application of Gibbs sampling using real data in animal breeding. An animal model was employed.

• J Jensen et al. (1994). Bayesian inference on variance and covariance components for traits influenced by maternal and direct genetic effects, using the Gibbs sampler. Acta. Agric. Scand., Sect. A, Animal Sci. 44:193-201.
  A Bayesian analysis of maternal and direct genetic effects.

• J Albert and S Chib. (1993). Bayesian analysis of binary and polychotomous response data. J. Am. Stat. Assoc. 88:669–679.
  The first Bayesian MCMC implementation of threshold models.

• DA Sorensen et al. (1995). Bayesian inference in threshold models using Gibbs sampling. Genet Sel Evol. 27:229-249.
  The first Bayesian treatment of ordered categories based on Gibbs sampling in animal breeding.

• CP Van Tassell and LD Van Vleck. (1996). Multiple-trait Gibbs sampler for animal models: flexible programs for Bayesian and likelihood-based (co)variance component inference. J Anim Sci. 74:2586-2597.
  Development of the MTGSAM software.

• LA García-Cortés and D Sorensen. (1997). On a multivariate implementation of the Gibbs sampler. Genet Sel Evol. 28:121-126.
  The first Bayesian treatment of multiple-traits animal models.

• J Jamrozik and LR Schaeffer. (1997). Estimates of genetic parameters for a test day model wit random regressions for yield traits of first lactation Holsteins. J Dairy Sci. 80:762-770.
  The first paper that applied Gibbs sampling to a random regression model.

• CP Van Tassell et al. (1998). Bayesian analysis of twinning and ovulation rates using a multiple-trait threshold model and Gibbs sampling. J Anim Sci. 76:2048-2061 .
  Extension of the MTGSAM to a multiple-trait threshold model.

• A Blasco. (2001). The Bayesian controversy in animal breeding. J Anim Sci. 79:2023-2046.
  A more recent review of Bayesian approaches in animal breeding.

• J Jamrozik. (2004). Implementation issues for Markov Chain Monte Carlo methods in random regression test-day models. J Anim Breed Genet. 121:1-13.
  This paper discusses problems related to the implementation of MCMC methods in dairy cattle.

• DA Sorensen. (2009). Developments in statistical analysis in quantitative genetics. Genetica 136:319-332.
  This is a nice overview of the application of MCMC in quantitative genetics.