Compilation for fast calculation over pedigrees.

Efficient computation of probabilistic relationships over family pedigrees is an important tool for a variety of problems in genetics, including genetic counseling and linkage analysis. The development of faster and more comprehensive algorithms has preoccupied geneticists for decades [?], and recent general-purpose algorithms for probabilistic inference over arbitrary networks (e.g., [?]) have also been proposed as useful tools for such problems [?]. We present a set of engineering speed-up methods developed as part of the implementation of a prototype program for assisting genetic counselors, geninfer-ii. The design of the underlying computational algorithm is due to Cooper [?], and treats the problem of finding an efficient way to evaluate a Bayes network as a problem of factoring algebraic formulæ. It is thus an extension of the method of [?] (though I believe it was independently formulated) and handles consanguinity by extending the factoring method rather than by cutset conditioning (as does, for example, [?]). The main arguments presented in this paper are: