Probabilistic Constraint Satisfaction with Non-Gaussian Noise
  We have previously reported a Bayesian algorithm for determining the
coordinates of points in three-dimensional space from uncertain constraints.
This method is useful in the determination of biological molecular structure.
It is limited, however, by the requirement that the uncertainty in the
constraints be normally distributed. In this paper, we present an extension of
the original algorithm that allows constraint uncertainty to be represented as
a mixture of Gaussians, and thereby allows arbitrary constraint distributions.
We illustrate the performance of this algorithm on a problem drawn from the
domain of molecular structure determination, in which a multicomponent
constraint representation produces a much more accurate solution than the old
single component mechanism. The new mechanism uses mixture distributions to
decompose the problem into a set of independent problems with unimodal
constraint uncertainty. The results of the unimodal subproblems are
periodically recombined using Bayes' law, to avoid combinatorial explosion. The
new algorithm is particularly suited for parallel implementation.
