A Bayesian Genomic Regression Model with Skew Normal Random Errors

Maximum a posteriori Threshold Genomic Prediction Model for Ordinal Traits

Due to the ever-increasing data collected in genomic breeding programs, there is a need for genomic prediction models that can deal better with big data. For this reason, here we propose a Maximum a posteriori Threshold Genomic Prediction (MAPT) model for ordinal traits that is more efficient than the conventional Bayesian Threshold Genomic Prediction model for ordinal traits. The MAPT performs the predictions of the Threshold Genomic Prediction model by using the maximum a posteriori estimation of the parameters, that is, the values of the parameters that maximize the joint posterior density. We compared the prediction performance of the proposed MAPT to the conventional Bayesian Threshold Genomic Prediction model, the multinomial Ridge regression and support vector machine on 8 real data sets. We found that the proposed MAPT was competitive with regard to the multinomial and support vector machine models in terms of prediction performance, and slightly better than the conventional Bayesian Threshold Genomic Prediction model. With regard to the implementation time, we found that in general the MAPT and the support vector machine were the best, while the slowest was the multinomial Ridge regression model. However, it is important to point out that the successful implementation of the proposed MAPT model depends on the informative priors used to avoid underestimation of variance components.

Genome-based prediction of Bayesian linear and non-linear regression models for ordinal data

Linear and non-linear models used in applications of genomic selection (GS) can fit different types of responses (e.g., continuous, ordinal, binary). In recent years, several genomic-enabled prediction models have been developed for predicting complex traits in genomic-assisted animal and plant breeding. These models include linear, non-linear and non-parametric models, mostly for continuous responses and less frequently for categorical responses. Several linear and non-linear models are special cases of a more general family of statistical models known as artificial neural networks, which provide better prediction ability than other models. In this paper, we propose a Bayesian Regularized Neural Network (BRNNO) for modelling ordinal data. The proposed model was fitted using a Bayesian framework; we used the data augmentation algorithm to facilitate computations. The proposed model was fitted using the Gibbs Maximum a Posteriori and Generalized EM algorithm implemented by combining code written in C and R programming languages. The new model was tested with two real maize datasets evaluated for Septoria and GLS diseases and was compared with the Bayesian Ordered Probit Model (BOPM). Results indicated that the BRNNO model performed better in terms of genomic-based prediction than the BOPM model.