In conventional linear models for whole-genome prediction and genome-wide association studies (GWAS), it is usually assumed that the relationship between genotypes and phenotypes is linear. Bayesian neural networks have been used to account for non-linearity such as complex genetic architectures. Here, we introduce a method named NN-Bayes, where "NN" stands for neural networks, and "Bayes" stands for Bayesian Alphabet models, including a collection of Bayesian regression models such as BayesA, BayesB, BayesC, Bayesian LASSO, and BayesR. NN-Bayes incorporates Bayesian Alphabet models into non-linear neural networks via hidden layers between SNPs and observed traits. Thus, NN-Bayes attempts to improve the performance of genome-wide prediction and GWAS by accommodating non-linear relationships between the hidden nodes and the observed trait, while maintaining genomic interpretability through the Bayesian regression models that connect the SNPs to the hidden nodes. For genomic interpretability, the posterior distribution of marker effects in NN-Bayes is inferred by Markov chain Monte Carlo (MCMC) approaches and used for inference of association through posterior inclusion probabilities (PIPs) and window posterior probability of association (WPPA). In a simulation study with dominance and epistatic effects, performance of NN-Bayes was significantly better than conventional linear models for both GWAS and whole-genome prediction, and the differences on prediction accuracy were substantial in magnitude. In real data analyses, for the soy dataset, NN-Bayes achieved significantly higher prediction accuracies than conventional linear models, and results from other four different species showed that NN-Bayes had similar prediction performance to linear models, which is potentially due to the small sample size. Our NN-Bayes is optimized for high-dimensional genomic data and implemented in an open-source package called "JWAS". NN-Bayes can lead to greater use of Bayesian neural networks to account for non-linear relationships due to its interpretability and computational performance.
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