  There is evidence that the numbers in probabilistic inference don't really
matter. This paper considers the idea that we can make a probabilistic model
simpler by making fewer distinctions. Unfortunately, the level of a Bayesian
network seems too coarse; it is unlikely that a parent will make little
difference for all values of the other parents. In this paper we consider an
approximation scheme where distinctions can be ignored in some contexts, but
not in other contexts. We elaborate on a notion of a parent context that allows
a structured context-specific decomposition of a probability distribution and
the associated probabilistic inference scheme called probabilistic partial
evaluation (Poole 1997). This paper shows a way to simplify a probabilistic
model by ignoring distinctions which have similar probabilities, a method to
exploit the simpler model, a bound on the resulting errors, and some
preliminary empirical results on simple networks.
