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Bayesian methods, such as BayesR, for predicting the genetic value or risk of individuals from their genotypes, such as Single Nucleotide Polymorphisms (SNP), are often implemented using a Markov Chain Monte Carlo (MCMC) process. However, the generation of Markov chains is computationally slow. We introduce a form of blocked Gibbs sampling for estimating SNP effects from Markov chains that greatly reduces computational time by sampling each SNP effect iteratively n-times from conditional block posteriors. Subsequent iteration over all blocks m-times produces chains of length m × n. We use this strategy to solve large-scale genomic prediction and fine-mapping problems using the Bayesian MCMC mixed-effects genetic model, BayesR3. We validate the method using simulated data, followed by analysis of empirical dairy cattle data using high dimension milk mid infra-red spectra data as an example of "omics" data and show its use to increase the precision of mapping variants affecting milk, fat, and protein yields relative to a univariate analysis of milk, fat, and protein. BayesR3 samples the polymorphisms affecting complex traits at reduced computational cost to predict the genetic value, breeding value, or individual risk of genotypes. [ABSTRACT FROM AUTHOR]

William G. Hill, universally known as Bill Hill, died on December 17, 2021, aged 81. Bill also compared the observed and predicted long-term response to selection and concluded that these data had little power to distinguish among different models for quantitative genetic variation, including the "infinitesimal model" that postulates a very large number of loci with very small effects (Hill 2010). Appropriately, John Sved and Bill wrote an insightful I Perspective i in Genetics reviewing 100 years of work on LD (Sved and Hill 2018). In particular, he was the first to quantify the role of new mutations in producing the variability needed for long-term continued responses to selection, which are such a remarkable feature of many artificial selection experiments and animal and plant breeding programs (Hill 1982a,b; Keightley and Hill 1983). [Extracted from the article]