Laplace's Method Approximations for Probabilistic Inference in Belief
  Networks with Continuous Variables
  Laplace's method, a family of asymptotic methods used to approximate
integrals, is presented as a potential candidate for the tool box of techniques
used for knowledge acquisition and probabilistic inference in belief networks
with continuous variables. This technique approximates posterior moments and
marginal posterior distributions with reasonable accuracy [errors are O(n^-2)
for posterior means] in many interesting cases. The method also seems promising
for computing approximations for Bayes factors for use in the context of model
selection, model uncertainty and mixtures of pdfs. The limitations, regularity
conditions and computational difficulties for the implementation of Laplace's
method are comparable to those associated with the methods of maximum
likelihood and posterior mode analysis.
