NAM (version 1.1.2)

Bayesian Gibbs Sampler: Bayesian Gibbs Sampler

Description

Univariate mixed model solver through Gibbs Sampling.

Usage

gibbs(y,X=NULL,Z=NULL,iK=NULL,Iter=1500,Burn=500,Thin=4,DF=5)

Arguments

y

Numeric vector of observations ($n$) describing the trait to be analyzed. NA is allowed.

X

Formula or incidence matrix ($n$ by $p$) for fixed effect. NA is not allowed.

Z

Formula or list of numeric matrix ($n$ by $p$) with incidence matrices for random effect. NA is not allowed.

iK

Numeric matrix or list of numeric matrices ($p$ by $p$) corresponding to the the inverse kinship matrix of each random effect with $p$ parameters.

Iter

Integer. Number of iterations or samples to be generated.

Burn

Integer. Number of iterations or samples to be discarted.

Thin

Integer. Thinning parameter, used to save memory by storing only one every 'Thin' samples.

DF

Integer. Hyper-parameter regarding degrees of freedom.

Value

• The function gibbs returns a list with variance components distribution a posteriori (Posterior.VC) and mode estimated (VC.mode), a list with the posterior distribution of regression coefficients (Posterior.Coef) and the posterior mode (Coef.mode) and mean (Coef.mean), and the fitted values using the mean (Fit.mean) and mode (Fit.mode) of posterior coefficients.

Details

Solve Gaussian mixed models in the Bayesian framework as described by Garc?a-Cort?s and Sorensen (1996) and Sorensen and Gianola, D. (2002) with conjugated priors. The hyper-prior solution for the scale parameter of inverse Chi squared is calculated as proposed by de los Campos et al. (2013).

References

de los Campos, G., Hickey, J. M., Pong-Wong, R., Daetwyler, H. D., and Calus, M. P. (2013). Whole-genome regression and prediction methods applied to plant and animal breeding. Genetics, 193(2), 327-345.

Garcia-Cortes, L. A., and Sorensen, D. (1996). On a multivariate implementation of the Gibbs sampler. Genetics Selection Evolution, 28(1), 121-126.

Sorensen, D., & Gianola, D. (2002). Likelihood, Bayesian, and MCMC methods in quantitative genetics. Springer Science & Business Media.

Examples

# Fitting Mixed Model
data(tpod)
S = seq(1,350,50)
test=gibbs(y,X=gen[,S],Z=~factor(fam))
plot(test$Fit.mean,y)

# Fitting GBLUP
K = tcrossprod(gen)
K = K/mean(diag(K))
iK = chol2inv(K)
test2=gibbs(y,iK=iK)
plot(test2$Fit.mean,y)