Approximate Bayesian computation (ABC) in practice (original) (raw)

Bayesian analysis of population structure based on linked molecular information

Mathematical Biosciences, 2007

The Bayesian model-based approach to inferring hidden genetic population structures using multilocus molecular markers has become a popular tool within certain branches of biology. In particular, it has been shown that heterogeneous data arising from genetically dissimilar latent groups of individuals can be effectively modelled using an unsupervised classification formulation. However, most currently employed models ignore potential linkage within the employed molecular information, and can therefore lead to biased inferences under certain circumstances. Utilizing the general theory of graphical models, we develop a framework that accounts for dependences both within linked molecular marker loci and DNA sequence data. Due to a high level of sequence conservation among eukaryotic species, the latter aspect is particularly relevant for analyzing rapidly evolving microbial species. The advantages of incorporating the dependence due to linkage in the classification models are illustrated by analyses of both simulated data and real samples of Bacillus cereus.

Back to Basics for Bayesian Model Building in Genomic Selection

Genetics, 2012

Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student’s t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known...