Conditional Independence in Statistical Theory

By A. P. Dawid. 1979

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “While causal structure discovery is hard if we have only two observables [190], the case of more observables is surprisingly easier, the reason being that, in that case, there are nontrivial conditional independence properties [52], [75], [238] implied by causal structure.”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Several other equivalent characterizations of conditional independence are given in Dawid (1979), for example.”
Towards Causal Representation Learning (2021, background): “While causal structure discovery is hard if we have only two observables [187], the case of more observables is surprisingly easier, the reason being that in that case, there are nontrivial conditional independence properties [238, 51, 74] implied by causal structure.”
Causality for Machine Learning (2019, background): “Surprisingly, this is not the case: the problem in a certain sense becomes easier, and the reason for this is that in that case, there are nontrivial conditional independence properties (Spohn, 1978; Dawid, 1979; Geiger and Pearl, 1990) implied by causal structure.”
The hardness of conditional independence testing and the generalised covariance measure (2018, background): “X ⊥ Y | Z if for all x, y, z with p(z) > 0, we have p(x, y|z) = p(x|z)p(y|z); see, for example, Dawid [17].”
Fast Conditional Independence Test for Vector Variables with Large Sample Sizes (2018, neutral): “A conditional independence test (CIT) extends this idea by testing for independence between two variables given the value of a third, or more generally, given the values of a set of further variables [Dawid, 1979].”
Kernel-based Conditional Independence Test and Application in Causal Discovery (2011, background): “Statistical independence and conditional independence (CI) are important concepts in statistics, artiﬁcial intelligence, and related ﬁelds (Dawid, 1979).”
Causal Markov condition for submodular information measures (2010, background): “The axiomatic approach to stochastic independence goes back to Dawid [9] who stated four axioms of conditional independence that are fulﬁlled for any kind of probability distribution.”
Causal inference in statistics: An overview (2009, neutral): “…readily be evaluated 18The notation Y ⊥ X |Z stands for the conditional independence relationship P (Y = y, X = x|Z = z) = P (Y = y|Z = z)P (X = x|Z = z) (Dawid, 1979). to yield P ∗(Yx = y) = ∑ z P ∗(Yx = y|z)P (z) = ∑ z P ∗(Yx = y|x, z)P (z) (using (39)) = ∑ z P ∗(Y = y|x, z)P (z) (using (36)) =…”
Strong completeness and faithfulness in Bayesian networks (1995, background): “Dawid, B. Larsen, and H. Leimer (1990). Independence properties of directed markov fields.”
Markov properties for mixed graphs (2011, methodology): “stribution P. We let XA =(Xv)v∈A etc. for each subset A of V . For disjoint subsets A, B, and C of V we use the short notation A ⊥⊥ B | C to denote that XA is conditionally independent of XB given XC [7, 19], that is, that for any measurable Ω⊆XA and P-almost all xB and xC, P(XA ∈Ω|XB =xB,XC =xC)=P(”
Graphical models for marked point processes based on local independence (2007, background): “he presence of N1 is conditionally independent of the past of N2 given the past of N1, or heuristically1 N1(t)⊥⊥F2 t−|F 1 t−, (2) where A⊥⊥B|C means ‘A is conditionally independent of B given C’ (cf. Dawid, 1979). For general processes, this is a stronger property than local independence but it hold”
Binary models for marginal independence (2007, methodology): “Graph 1(b) does not imply any independence restrictions relating the observed variables, whereas graph 1(a) implies that A1 ⊥⊥D2 and A2 ⊥⊥D1, .1/ using the notation of Dawid (1979).”
Matching on the Estimated Propensity Score (2016, background): “Assumption 1(i) uses the conditional independence notation in Dawid (1979). This assumption is often referred to as “unconfoundedness”. It will hold, for example, if all confounders are included in X, so that after controlling for X, treatment exposure is independent of the potential outcomes. Hahn ”
A Bayesian view of doubly robust causal inference (2016, unknown): “In this case Si is sufficient to control for confounding, since from the properties of conditional independence (Dawid, 1979) it follows that (Y0i,Y1i) ⊥ Zi |Si.”
Testing conditional independence for continuous random variables (2004, methodology): “Following Dawid (1979), this hypothesis is denoted as Y⊥ Z|X.”
Bayesian inference for non‐stationary spatial covariance structure via spatial deformations (2003, background): “It can be shown that this parameter is unidentifiable in the sense of Dawid (1979).”
Sensitivity of Propensity Score Methods to the Specifications (2008, unknown): “…due to observables is formally characterized by the following two assumptions: M-1: 0 1 ( , ) | Y Y T X & Unconfoundedness assumption M-2: 0 ( 1| ) 1 prob T X = Common-support assumption where & is the notation for statistical independence as in Dawid (1979), and prob stands for probability.”