On the Geometry of Bayesian Graphical Models with Hidden Variables

2013/01/30 by Raffaella Settimi, Settimi, Raffaella, Jim Q. Smith +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1301.7411

openalex publication_date 2013/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain insights in the nature of the unidentifiability inherent in such models, the way posterior densities will be sensitive to prior densities and the typical geometrical form these posterior densities might take. Many of these insights carry over into more complicated Bayesian networks with systematic missing data.

Citations

• Learning Bayesian Networks from Incomplete Databases

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