Estimating deterministic parameters by Bayesian inference with emphasis on estimating the uncertainty of the parameters

Abstract

Parameter estimation is generally based upon the maximum likelihood procedure which often requires regularization, particularly for non-linear models, and cannot account for nuisance variables or unacceptable regions of parameter values. Bayesian inference can address both difficulties but is computationally expensive and open to questions about the appropriateness of the prior knowledge and when probability densities employed. An approach developed by Banks which is a cross between these methods has been successfully employed with equivalent computational costs. This article compares the three approaches for a simple non-linear test problem.