Abstract
Making inference on population structure from genotype data requires to identify the actual subpopulations and assign individuals to these populations. The source populations are assumed to be in Hardy-Weinberg equilibrium, but the allelic frequencies of these populations and even the number of populations present in a sample are unknown. In this chapter we present a review of some Bayesian parametric and nonparametric models for making inference on population structure, with emphasis on model-based clustering methods. Our aim is to show how recent developments in Bayesian nonparametrics have been usefully exploited in order to introduce natural nonparametric counterparts of some of the most celebrated parametric approaches for inferring population structure. We use data from the 1000 Genomes project (http://www.1000genomes.org/) to provide a brief illustration of some of these nonparametric approaches.
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Acknowledgements
We would like to thank Kaustubh Adhikari for kindly providing the pahsed data and Lloyd Elliott for developing user-friendly MATLAB functions for the linked hierarchical Dirichlet process. Stefano Favaro is supported by the European Research Council (ERC) through StG N-BNP 306406. Yee Whye Teh is supported by the European Research Council (ERC) through the European Unions Seventh Framework Programme (FP7/2007–2013) ERC grant agreement 617411.
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De Iorio, M., Favaro, S., Teh, Y.W. (2015). Bayesian Inference on Population Structure: From Parametric to Nonparametric Modeling. In: Mitra, R., Müller, P. (eds) Nonparametric Bayesian Inference in Biostatistics. Frontiers in Probability and the Statistical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-19518-6_7
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