Gaussian Conditional Independence Relations Have No Finite Complete Characterization
نویسنده
چکیده
We show that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables. To do this, we construct, for each n > 3 a family of n conditional independence statements on n random variables which together imply that X1⊥X2, and such that no subset have this same implication. The proof relies on binomial primary decomposition.
منابع مشابه
Conditional Independence Relations Have No Finite Complete Characterization
The hypothesis of existence of a nite characterization of conditional{independence relations (CIRs) is refused. This result is shown to be equivalent with the non{existence of a simple deductive system describing relationships among CI{statements (it is certain type of syntactic description). However, under the assumption that CIRs are grasped the existence of a countable characterization of CI...
متن کاملClasses of Gaussian, Discrete and Binary Representable Independence Models Have No Finite Characterization
The paper shows that there is no finite set of forbidden minors which characterizes classes of independence models that are representable by Gaussian, discrete and binary distributions, respectively. In addition, a way to prove the nonexistence of a finite characterization for any other class of independence models is suggested. MSC 2000: 60A99, 68T30, 94A15
متن کاملConditional independence and natural conditional functions
The concept of conditional independence (CI) within the framework of natural conditional functions (NCFs) is studied. An NCF is a function ascribing natural numbers to possible states of the world; it is the central concept of Spohn's theory of deterministic epistemology. Basic properties of CI within this framework are recalled, and further results analogous to the results concerning probabili...
متن کاملConditional Dependence in Longitudinal Data Analysis
Mixed models are widely used to analyze longitudinal data. In their conventional formulation as linear mixed models (LMMs) and generalized LMMs (GLMMs), a commonly indispensable assumption in settings involving longitudinal non-Gaussian data is that the longitudinal observations from subjects are conditionally independent, given subject-specific random effects. Although conventional Gaussian...
متن کاملA Transformational Characterization of Markov Equivalence for Directed Maximal Ancestral Graphs
The conditional independence relations present in a data set usually admit multiple causal explanations — typically represented by directed graphs — which are Markov equivalent in that they entail the same conditional independence relations among the observed variables. Markov equivalence between directed acyclic graphs (DAGs) has been characterized in various ways, each of which has been found...
متن کامل