An important class of continuous Bayesian networks are those that have linear conditionally deterministic variables (a variable that is a linear deterministic function of its parents). In this case, the joint density function for the variables in the network does not exist. Conditional linear Gaussian (CLG) distributions can handle such cases when all variables are normally distributed. In this paper, we develop operations required for performing inference with linear conditionally deterministic variables in continuous Bayesian networks using relationships derived from joint cumulative distribution functions (CDF’s). These methods allow inference in networks with linear deterministic variables and non-Gaussian distributions.
Cobb, B. R., and P. P. Shenoy, "Operations for inference in continuous Bayesian networks with linear deterministic variables," International Journal of Approximate Reasoning, Vol. 42, Nos. 1--2, May 2006, pp. 21--36.
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