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B0206
Title: Bayesian nonparametric approaches to quantifying dependence between random variables Authors:  Sarah Filippi - University of Oxford (United Kingdom) [presenting]
Chris Holmes - University of Oxford (United Kingdom)
Luis E Nieto-Barajas - ITAM (Mexico)
Abstract: Nonparametric and nonlinear measures of statistical dependence between pairs of random variables have proved themselves important tools in modern data analysis, where the emergence of large data sets can support the relaxation of linearity assumptions implicit in traditional association scores such as correlation. We will present two Bayesian nonparametric procedures to test for dependences. In the first one a tractable, explicit and analytic quantification of the relative evidence of dependence vrs independence, using Polya tree priors on the space of probability measures which can then be embedded within a decision theoretic test for dependence. In the second procedure the unknown sampling distribution is specified via Dirichlet Process Mixtures (DPM) of Gaussians, which provide great flexibility while also encompassing smoothness assumptions. These procedures can accommodate known uncertainty in the form of the underlying sampling distribution and provides an explicit posterior probability measure of both dependence and independence. Well-known advantages of having an explicit probability measure include the easy comparison of evidence across different studies, the inclusion of prior information, and the integration of results within formal decision analysis.