2007/04/21 by Seth Sullivant, Sullivant, Seth
Computer Science · Mathematics · #Advanced Algebra and Logic #Bayesian Modeling and Causal Inference #Commutative Algebra (math.AC) #FOS: Mathematics #Probability (math.PR) #Rough Sets and Fuzzy Logic #math.AC #math.PR
paper · pdf · doi:10.48550/arxiv.0704.2847
6 pages
arxiv created 2007/04/21 · openalex publication_date 2007/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \ind X2, and such that no subset have this same implication. The proof relies on binomial primary decomposition.