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The fully conditional posterior densities for the multilocus association model (1) parameters are as follows.

The derivations of the fully conditional posterior densities of the multilocus association model are presented in the Appendix A1.

An advantage of the G-BLUP over the multilocus association model is that no preselection of the markers is needed.

Contrary to G-BLUP, a multilocus association model uses the marker information directly by assigning different, possibly zero, effects to the marker genotypes.

With the 100 Gaussian QTL-MAS data replicates, the multilocus association model produces an average correlation 0.89 whereas the G-BLUP produces an average correlation 0.80.

The number of markers selected to the multilocus association model can be tuned into an optimal value similarly to the prior parameters.

Additionally, multilocus association models with different shrinkage or variable selection mechanisms may be able to cope with different amount of oversaturation.

A relatively recent contender for the BLUP-type of model in the genomic selection field is to apply simultaneous estimation and variable selection or variable regularization to multilocus association models (e.g., Meuwissen et al. 2001; Xu 2003).

Furthermore, the threshold approach for censored observations has been considered by Broman (2003), within BLUP context by Sorensen et al. (1998), and with multilocus association models by Sillanpää and Hoti (2007) and Iwata et al. (2009).

Multilocus association models of binary and ordinal traits have been considered by Hoti and Sillanpää (2006), Iwata et al. (2009), González-Recio et al. (2009), González-Recio and Forni (2011), and Wang et al. (2013).

In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models.