Variance parameters in additive models are typically assigned independent priors that do not account for model structure. We present a new framework for prior selection based on a hierarchical decomposition of the total variance along a tree structure to the individual model components. For each split in the tree, an analyst may be ignorant or have a sound intuition on how to attribute variance to the branches. In the former case a Dirichlet prior is appropriate to use, while in the latter case a penalised complexity (PC) prior provides robust shrinkage. A bottom-up combination of the conditional priors results in a proper joint prior. We suggest default values for the hyperparameters and offer intuitive statements for eliciting the hyperparameters based on expert knowledge. The prior framework is applicable for R packages for Bayesian inference such as INLA and RStan.Three simulation studies show that, in terms of the application-specific measures of interest, PC priors improve inference over Dirichlet priors when used to penalise different levels of complexity in splits. However, when expressing ignorance in a split, Dirichlet priors perform equally well and are preferred for their simplicity. We find that assigning current state-of-the-art default priors for each variance parameter individually is less transparent and does not perform better than using the proposed joint priors. We demonstrate practical use of the new framework by analysing spatial heterogeneity in neonatal mortality in Kenya in 2010-2014 based on complex survey data.

We propose a novel Bayesian approach that robustifies genomic modelling by leveraging expert knowledge through prior distributions. The central component is the hierarchical decomposition of phenotypic variation into additive and non-additive genetic variation, which leads to an intuitive model parameterization that can be visualised as a tree. The edges of the tree represent ratios of variances, for example broad-sense heritability, which are quantities for which expert knowledge is natural to exist. Penalized complexity priors are defined for all edges of the tree in a bottom-up procedure that respects the model structure and incorporates expert knowledge through all levels. We investigate models with different sources of variation and compare the performance of different priors implementing varying amounts of expert knowledge in the context of plant breeding. A simulation study shows that the proposed priors implementing expert knowledge improve the robustness of genomic modelling and the selection of the genetically best individuals in a breeding program. We observe this improvement in both variety selection on genetic values and parent selection on additive values; the variety selection benefited the most. In a real case study expert knowledge increases phenotype prediction accuracy for cases in which the standard maximum likelihood approach did not find optimal estimates for the variance components. Finally, we discuss the importance of expert knowledge priors for genomic modelling and breeding, and point to future research areas of easy-to-use and parsimonious priors in genomic modelling.

A major challenge with modelling non-additive genetic variation is that it is hard to separate nonadditive variation from additive and environmental variation. In this paper, we describe how to alleviate this issue, and improve genomic modelling of additive and non-additive variation, by leveraging the ample expert knowledge available about the relative magnitude of the sources of phenotypic variation. The method is Bayesian and uses the recently introduced penalized complexity and hierarchical decomposition prior frameworks, where priors can be specified and visualized in an intuitive way, and be used to induce parsimonious modelling. We evaluate the potential impact for plant breeding through a simulated case study of a wheat breeding program. We compare different models and different priors with varying amounts of expert knowledge. The results show that the proposed priors and expert knowledge improved the robustness of the genomic modelling and the selection of the genetically best individuals in the breeding program. We observed this improvement in both variety selection on genetic values and parent selection on additive values, but the variety selection benefited the most. An improvement was not observed in the overall accuracy of estimating genetic values for all individuals and variance components. Finally, we discuss the importance of expert-knowledge priors for genomic modelling and breeding, and point to future research areas of easy-to-use and parsimonious priors in genomic modelling.

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The spike-timing dependent plasticity (STDP) learning rules are popular in both neuroscience and computer algorithms due to their ability to capture the change in neural connections arising from the correlated activity of neurons. Recent advances in recording technology have made large neural recordings common, but to date, there is no established method for inferring unobserved neural connections and learning rules from them. We use a Bayesian framework and assume neural spike recordings follow a binary data model to infer the connections and their evolution over time from data using STDP rules. We test the resulting method on one simulated and one real case study, where the real case study consists of human electrophysiological recordings. The simulated case study allows validation of the model, and the real case study shows that we are able to infer learning rules from awake human data that align with experimental results in rats and other animals. The real case study also uncovered a trend in maximum synaptic modification and age, however, this will need testing on a larger scale to draw conclusions.