Abstract

Bayesian hierarchical models with additive latent structures are popular since additivity simplifies interpretation and inference. However, the common choice of independent priors on the variances of the model components result in haphazard a priori control on the total variance and how it is attributed to the model components. We propose a joint prior for the variance parameters that explicitly controls the total variance and how it is distributed to the model components. For latent Gaussian models, we can utilize the penalized complexity prior framework to achieve the desired shrinkage between the random effects in the model, or we can choose to be ignorant through Dirichlet priors. The resulting priors have intuitive hyperparameters and are weakly-informative.

In the field of plant breeding, geneticists have strong expert knowledge on the relative sizes of the different genetic effects: additive, dominant and epistasis. We demonstrate how one can intuitively incorporate this knowledge in the model in a robust way, and how the prior knowledge can be communicated between geneticists and statisticians through a visualization of the prior assumptions. We show through a simulated breeding program of wheat that our method, which takes advantage of the expert knowledge on additive, dominant and epistasis effects in the analysis, performs better, in terms of genomic selection and robustness, than standard methods using only additive effects.

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