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This section describes inference in continuous and hybrid Bayesian networks, i.e., networks including both discrete and continuous variables. There are two algorithms that GeNIe relies on in such networks: (1) hybrid forward sampling and (2) discretization.

Hybrid forward sampling is used whenever there is no evidence in the network or all evidence is in parent-less nodes. In that case, stochastic forward sampling is very efficient and its complexity is polynomial in the number of nodes. Whenever there is evidence in nodes with parents, forward sampling runs into the theoretical problem of very unlikely evidence. Samples involving the observed values become extremely unlikely, approaching zero probability.

GeNIe's answer to this problem is converting the hybrid network into a discrete Bayesian network for the purpose of inference. This is accomplished by discretizing every continuous variable in the model, according to the discretization intervals specified by the user or, if no discretization is specified, GeNIe offers a crude discretization that the user can refine further. The discretized network offers insight into the continuous posterior marginal distributions over the variables of interest. GeNIe puts no limitations on the functional forms of the interactions between variables in the model, offering its user a complete modeling freedom.

The following two sections describe the details of these two approaches.