We consider probabilistic inference in general hybrid
networks, which include continuous and discrete variables in
an arbitrary topology. We reexamine the question of variable
discretization in a hybrid network aiming at minimizing the
information loss induced by the discretization. We show that
a nonuniform partition across all variables as opposed to
uniform partition of each variable separately reduces the size
of the data structures needed to represent a continuous
function. We also provide a simple but efficient procedure
for nonuniform partition. To represent a nonuniform
discretization in the computer memory, we introduce a new data
structure, which we call a Binary Split Partition (BSP) tree.
We show that BSP trees can be an exponential factor smaller
than the data structures in the standard uniform
discretization in multiple dimensions and show how the BSP
trees can be used in the standard join tree algorithm. We
show that the accuracy of the inference process can be
significantly improved by adjusting discretization with
evidence. We construct an iterative anytime algorithm that
gradually improves the quality of the discretization and the
accuracy of the answer on a query. We provide empirical
evidence that the algorithm converges.