How to convert nonlinear functions to piecewise linear ones.

What is it about?

If you have a Bayesian network with X_1 that has a chi-sq(m) distribution, and an independent variable X_2 with chi-sq(n) distribution, and Y = (X_1/m)/(X_2/n), then what is the marginal distribution of Y? For this special case, we know that Y is distributed as F(m, n), but out method can automatically deduce the distribution of Y. The conditional distribution of Y is deterministic as the conditional variance is 0, and the relationship of Y to X_1 and X_2 is nonlinear.

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Why is it important?

The method described in this paper describes how one can make inferences in Bayesian networks with nonlinear deterministic conditional distributions by first approximating the nonlinear deterministic functions to piecewise linear ones.