Symbolic Probabilistic Inference with Continuous Variables
  Research on Symbolic Probabilistic Inference (SPI) [2, 3] has provided an
algorithm for resolving general queries in Bayesian networks. SPI applies the
concept of dependency directed backward search to probabilistic inference, and
is incremental with respect to both queries and observations. Unlike
traditional Bayesian network inferencing algorithms, SPI algorithm is goal
directed, performing only those calculations that are required to respond to
queries. Research to date on SPI applies to Bayesian networks with
discrete-valued variables and does not address variables with continuous
values. In this papers, we extend the SPI algorithm to handle Bayesian networks
made up of continuous variables where the relationships between the variables
are restricted to be ?linear gaussian?. We call this variation of the SPI
algorithm, SPI Continuous (SPIC). SPIC modifies the three basic SPI operations:
multiplication, summation, and substitution. However, SPIC retains the
framework of the SPI algorithm, namely building the search tree and recursive
query mechanism and therefore retains the goal-directed and incrementality
features of SPI.
