In Computing Science and Statistics 27, M. M. Meyer and J. L. Rosenberger, eds., pp. 202-211 (Interface Foundation, Fairfax, VA 22039-7400, 1996)

A computational approach to Bayesian inference

Kenneth M. Hanson and Gregory S. Cunningham
Los Alamos National Laboratory


Although the Bayesian approach provides a complete solution to model-based analysis, it is often difficult to obtain closed-form solutions for complex models. However, numerical solutions to Bayesian modeling problems are now becoming attractive because of the advent of powerful, low-cost computers and new algorithms. We describe a general-purpose implementation of the Bayesian methodology on workstations that can deal with complex nonlinear models in a very flexible way. The models are represented by a data-flow diagram that may be manipulated by the analyst through a graphical-programming environment that is based on a fully object-oriented design. Maximum a posteriori solutions are achieved using a general optimization algorithm. A new technique for estimating and visualizing the uncertainties in specific aspects of the model is incorporated.

Keywords: Bayesian analysis, MAP estimator, uncertainty estimation, object-oriented programming, adjoint differentiation, optimization

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