Reply to 'Comments on Froehner's Bayesian Formulation for Data Evaluation'

摘要

For evaluation of discrepant data with unrecognized ("negligence") errors, Y.-A. Chao advocates the approach he presented in his Refs. 4 and 5 as a simple alternative to what I discussed in his Refs. 1, 2, and 3. As he correctly points out, we both use entropy maximization to set up Gaussian probability distributions for unknown errors, but the problems we consider are not quite the same. Discrepancies due to unrecognized errors are discussed only in Ref. 3, whereas Ref. 1 is devoted to the correlations induced by recognized common ("systematic") errors and Ref. 2 to uncertainty assignment in general. The problem I considered in Chao's Ref. 3 is as follows: Several uncorrelated measurements of a quantity μ yielded reported data x_1 +- σ_1, ... , x_n +- σ_n (which we write summarily as n-dimensional sample-space vectors x ≡ {x_1, ... , x_n} and σ ≡ {σ_1, ... , σ_n}).What is the best estimate for μ if the data do not agree "within error bars?" As always in parameter estimation, one starts by writing down the probability distribution for all incompletely known quantities.