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Bayesian Dependence Tests for Continuous, Binary and Mixed Continuous-Binary Variables

Dalle Molle Institute for Artificial Intelligence, Manno 6928, Switzerland
School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast BT7 1NN, UK
Author to whom correspondence should be addressed.
Academic Editors: Julio Stern and Adriano Polpo
Entropy 2016, 18(9), 326;
Received: 20 June 2016 / Revised: 25 August 2016 / Accepted: 26 August 2016 / Published: 6 September 2016
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
Tests for dependence of continuous, discrete and mixed continuous-discrete variables are ubiquitous in science. The goal of this paper is to derive Bayesian alternatives to frequentist null hypothesis significance tests for dependence. In particular, we will present three Bayesian tests for dependence of binary, continuous and mixed variables. These tests are nonparametric and based on the Dirichlet Process, which allows us to use the same prior model for all of them. Therefore, the tests are “consistent” among each other, in the sense that the probabilities that variables are dependent computed with these tests are commensurable across the different types of variables being tested. By means of simulations with artificial data, we show the effectiveness of the new tests. View Full-Text
Keywords: dependence; Bayesian independence test; Dirichlet Process dependence; Bayesian independence test; Dirichlet Process
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Benavoli, A.; De Campos, C.P. Bayesian Dependence Tests for Continuous, Binary and Mixed Continuous-Binary Variables. Entropy 2016, 18, 326.

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