Extended Maximum Likelihood vs Maximum Likelihood ; Error Estimates on Quantitative Bayesian Priors

This document updates the analysis of errors found in Tina Memo 2010-008. In particular we show that the errors presented there are exact for EML interpretations of parameter estimates, but only an approximation for conventional Likelihood. The work explains the error model used in Tina Memo 2000-007, for the analysis of distribution of cranial fluid as measured in a volumetric segmentation of MR images. This document provides useful insights into the practical distinctions which must be made between the two alternative definitions of Likelihood, with regard to parameter estimation and the use of algorithms such as EM. 1 Bayes Theorem and the EM Cost Function Given a set of probability densities, P (X|k), for data generation processes, k ∈ K, over some pattern space X, Bayes Theorem can be applied to determine the probability that a given observed pattern, X, was generated by any particular process: P (k|X) = P (X|k)P (k)