SYMBOLIC PROBABILISTIC INFERENCE WITH BOTH DISCRETE AND CONTINUOUS-VARIABLES

The importance of resolving general queries in Bayesian networks has b een the focus of attention in recent research on the Symbolic Probabil istic Inference (SPI) algorithm [4], [5], SPI applies the concept of d ependency-directed backward search to probabilistic inference, and is incremental with respect to both queries and observations. Unlike trad itional Bayesian network inferencing algorithms, the SPI algorithm is goal directed, performing only those calculations that are required to respond to queries. Research to date on SPI applies to Bayesian netwo rks with only discrete-valued variables or only continuous variables ( linear Gaussian) [3] and does not address networks with both discrete and continuous variables. In this paper, we extend the SPI algorithm t o handle Bayesian networks made up of both discrete and continuous var iables (SPI-DC). The only topological constraint of the networks is th at the successors of any continuous variable have to be continuous var iables as well. In order to have exact analytical solution, the relati onships between the continuous variables are restricted to be ''linear Gaussian.'' With new representation, SPI-DC modifies the three basic SPI operations: multiplication, summation, and substitution. However, SPI-DC retains the framework of the SPI algorithm, namely building the search tree and recursive query mechanism and therefore retains the g oal-directed and incrementality features of SPI.