{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:51Z","timestamp":1760242851992,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2016,9,6]],"date-time":"2016-09-06T00:00:00Z","timestamp":1473120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u201cconsistent\u201d 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.<\/jats:p>","DOI":"10.3390\/e18090326","type":"journal-article","created":{"date-parts":[[2016,9,6]],"date-time":"2016-09-06T10:10:16Z","timestamp":1473156616000},"page":"326","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bayesian Dependence Tests for Continuous, Binary and Mixed Continuous-Binary Variables"],"prefix":"10.3390","volume":"18","author":[{"given":"Alessio","family":"Benavoli","sequence":"first","affiliation":[{"name":"Dalle Molle Institute for Artificial Intelligence, Manno 6928, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cassio","family":"De Campos","sequence":"additional","affiliation":[{"name":"School of Electronics, Electrical Engineering and Computer Science, Queen\u2019s University Belfast, Belfast BT7 1NN, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.2307\/271063","article-title":"Bayesian model selection in social research","volume":"25","author":"Raftery","year":"1995","journal-title":"Sociol. 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