2015/06/02 by Sarah Filippi, Chris Holmes, Filippi, Sarah +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gene expression and cancer classification #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1506.00829
openalex publication_date 2015/06/02 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Nonparametric and nonlinear measures of statistical dependence between pairs\nof random variables are important tools in modern data analysis. In particular\nthe emergence of large data sets can now support the relaxation of linearity\nassumptions implicit in traditional association scores such as correlation.\nHere we describe a Bayesian nonparametric procedure that leads to a tractable,\nexplicit and analytic quantification of the relative evidence for dependence vs\nindependence. Our approach uses Polya tree priors on the space of probability\nmeasures which can then be embedded within a decision theoretic test for\ndependence. Polya tree priors can accommodate known uncertainty in the form of\nthe underlying sampling distribution and provides an explicit posterior\nprobability measure of both dependence and independence. Well known advantages\nof having an explicit probability measure include: easy comparison of evidence\nacross different studies; encoding prior information; quantifying changes in\ndependence across different experimental conditions, and; the integration of\nresults within formal decision analysis.\n