Uncertainty estimates for the Bayes Inference Engine, (BIE)
Thomas A Beery · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2009
In the fall 2007 meeting of the BIB users group, two approaches to making uncertainty estimates were presented. Ken Hanson asserted that if the BFGS optimizer was used, the inverse Hessian matrix was the same as the covariance matrix representing parameter uncertainties. John Pang presented preliminary results of a Monte Carlo method called Randomized Maximum Likelihood (RML). The BFGS/Hessian matrix approach may be applied to the region of the 'ideal model' Approximately 250 parameters describing the object density patches that are varied to match an image of 1,000,000 pixels. I cast this in terms of least squares analysis, as it is much better understood. This not as large a conceptual jump as some suppose because many of the functional blocks in the BIB are taken directly from existing least squares programs. If a Gaussian (normal) probability density function is assumed for both the observation and parameter errors, the Bayesian and least squares result should be identical.