2020
DOI: 10.3934/fods.2020009
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A Bayesian nonparametric test for conditional independence

Abstract: This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Pólya tree priors on spaces of conditional probability densities, accounting for uncertainty in the form of the underlying distributions in a nonparametric way. The Bayesian perspective provides an inherently symmetric probability measure of conditional dependence or independence, a feature particularly … Show more

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Cited by 2 publications
(6 citation statements)
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“…We now propose a novel conditional independence test of the type C |= X|Z, where X and Z are continuous one-dimensional random variables and C is a binary variable. We combine elements of both the two-sample test proposed by Holmes et al (2015), and a conditional independence test from Teymur and Filippi (2019). The conditional independence test from Teymur and Filippi (2019) Given n draws {(C 1 , X 1 , Z 1 ), ..., (C n , X n , Z n )} from binary variable C and continuous onedimensional random variables X and Z, define X (0) := {X i : C i = 0, i ∈ {1, .., n}} and X (1) := {X i : C i = 1, i ∈ {1, .., n}}.…”
Section: A Nonparametric Conditional Two-sample Testmentioning
confidence: 99%
See 4 more Smart Citations
“…We now propose a novel conditional independence test of the type C |= X|Z, where X and Z are continuous one-dimensional random variables and C is a binary variable. We combine elements of both the two-sample test proposed by Holmes et al (2015), and a conditional independence test from Teymur and Filippi (2019). The conditional independence test from Teymur and Filippi (2019) Given n draws {(C 1 , X 1 , Z 1 ), ..., (C n , X n , Z n )} from binary variable C and continuous onedimensional random variables X and Z, define X (0) := {X i : C i = 0, i ∈ {1, .., n}} and X (1) := {X i : C i = 1, i ∈ {1, .., n}}.…”
Section: A Nonparametric Conditional Two-sample Testmentioning
confidence: 99%
“…(5) Teymur and Filippi (2019) utilise conditional optional Pólya tree (cond-OPT) priors (Ma, 2017) for modelling conditional densities of the form f X|Z (x|z). As we require an expression for the marginal likelihoods of X|Z, X (0) |Z and X (1) |Z, we briefly review the construction of the cond-OPT.…”
Section: A Nonparametric Conditional Two-sample Testmentioning
confidence: 99%
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