Exploring the reliability of Bayesian reconstructions

Kenneth M. Hanson; Gregory S. Cunningham

doi:10.1117/12.208713

12 May 1995 Exploring the reliability of Bayesian reconstructions

Kenneth M. Hanson, Gregory S. Cunningham

Proceedings Volume 2434, Medical Imaging 1995: Image Processing; (1995) https://doi.org/10.1117/12.208713
Event: Medical Imaging 1995, 1995, San Diego, CA, United States

Abstract

The Bayesian approach allows one to combine measurement data with prior knowledge about models of reality to draw inferences about the validity of those models. The posterior probability quantifies the degree of certainty one has about those models. We propose a method to explore the reliability, or uncertainty, of specific features of a Bayesian solution. If on draws an analogy between the negative logarithm of the posterior and a physical potential, the gradient of this potential can be interpreted as a force that acts on the model. As model parameters are perturbed from their maximum a posteriori (MAP) values, the strength of the restoring force that drives them back to the MAP solution is directly related to the uncertainty in those parameter estimates. The correlations between the uncertainties of parameter estimates can be elucidated.

Citation Download Citation

Kenneth M. Hanson and Gregory S. Cunningham "Exploring the reliability of Bayesian reconstructions", Proc. SPIE 2434, Medical Imaging 1995: Image Processing, (12 May 1995); https://doi.org/10.1117/12.208713

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