Use of the reversible jump Markov chain Monte Carlo algorithm to select multiplicative terms in the AMMI-Bayesian model.

The model selection stage has become a central theme in applying the additive main effects and multiplicative interaction (AMMI) model to determine the optimal number of bilinear components to be retained to describe the genotype-by-environment interaction (GEI). In the Bayesian context, this problem has been addressed by using information criteria and the Bayes factor. However, these procedures are computationally intensive, making their application unfeasible when the model's parametric space is large.

Shrinkage in the Bayesian analysis of the GGE model: A case study with simulation.

The genotype main effects plus the genotype × environment interaction effects model has been widely used to analyze multi-environmental trials data, especially using a graphical biplot considering the first two principal components of the singular value decomposition of the interaction matrix. Many authors have noted the advantages of applying Bayesian inference in these classes of models to replace the frequentist approach. This results in parsimonious models, and eliminates parameters that would be present in a traditional analysis of bilinear components (frequentist form).

Functional models in genome-wide selection.

The development of sequencing technologies has enabled the discovery of markers that are abundantly distributed over the whole genome. Knowledge about the marker locations in reference genomes provides further insights in the search for causal regions and the prediction of genomic values. The present study proposes a Bayesian functional approach for incorporating the marker locations into genomic analysis using stochastic methods to search causal regions and predict genotypic values.

Bayesian factor analytic model: An approach in multiple environment trials.

One of the main challenges in plant breeding programs is the efficient quantification of the genotype-by-environment interaction (GEI). The presence of significant GEI may create difficulties for breeders in the selection and recommendation of superior genotypes for a wide environmental network. Among the diverse statistical procedures developed for this purpose, we highlight those based on mixed models and factor analysis that are called factor analytic (FA) models.

Genome-wide association analysis of ear rot resistance caused by Fusarium verticillioides in maize.

The identification of causal regions associated with resistance to Fusarium verticillioides can be useful to understand resistance mechanisms and further be used in breeding programs. In this study, a genome-wide association study (GWAS) was conducted to identify candidate markers associated with resistance to the ear rot caused by the fungus F. verticillioides.