2013/01/10 by Tim Van Allen, Van Allen, Tim, Russell Greiner +3
Computer Science · Engineering · #Anomaly Detection Techniques and Applications #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Fault Detection and Control Systems
paper · pdf · doi:10.48550/arxiv.1301.2313
openalex publication_date 2013/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Bayesian Belief Network (BN) is a model of a joint distribution over a setof n variables, with a DAG structure to represent the immediate dependenciesbetween the variables, and a set of parameters (aka CPTables) to represent thelocal conditional probabilities of a node, given each assignment to itsparents. In many situations, these parameters are themselves random variables - this may reflect the uncertainty of the domain expert, or may come from atraining sample used to estimate the parameter values. The distribution overthese "CPtable variables" induces a distribution over the response the BNwill return to any "What is Pr(H | E)?" query. This paper investigates thevariance of this response, showing first that it is asymptotically normal,then providing its mean and asymptotical variance. We then present aneffective general algorithm for computing this variance, which has the samecomplexity as simply computing the (mean value of) the response itself - ie,O(n 2w), where n is the number of variables and w is the effective treewidth. Finally, we provide empirical evidence that this algorithm, whichincorporates assumptions and approximations, works effectively in practice,given only small samples.