Integration of Hierarchical Models

Valen E. Johnson
Duke University

Nov 30 1989

A technique called quantile integration is proposed for the integration of hierarchical models. If n denotes the number of points used to evaluate the integral, the error of approximation if O(log(n)/n) when the moment generating function exists for each conditional density apeparing the model, and is O(n-1+1/k) when each conditional density possesses k moments. Approximations produced by the technique take the form of probability density functions, and the method requires no modification for densities defined on bounded or semi-bounded intervals. In many models, computational requirements increase only linearly with the dimension of the integral, and little analytical effort is needed for implementation.


PDF icon 1989-07.pdf