On the Least-Squares Fitting of Correlated Data:a Priorivsa PosterioriWeighting

✍ Scribed by Joel Tellinghuisen

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 484 KB
• Volume: 179
• Category: Article
• ISSN: 0022-2852
• DOI: 10.1006/jmsp.1996.0208

✦ Synopsis

One of the methods in common use for analyzing large data sets is a two-step procedure, in which subsets of the full data are first least-squares fitted to a preliminary set of parameters, and the latter are subsequently merged to yield the final parameters. The second step of this procedure is properly a correlated least-squares fit and requires the variancecovariance matrices from the first step to construct the weight matrix for the merge. There is, however, an ambiguity concerning the manner in which the first-step variance-covariance matrices are assessed, which leads to different statistical properties for the quantities determined in the merge. The issue is one of a priori vs a posteriori assessment of weights, which is an application of what was originally called internal vs external consistency by Birge [Phys. Rev. 40, 207-227 (1932)] and Deming (''Statistical Adjustment of Data. '' Dover, New York, 1964). In the present work the simplest case of a merge fit-that of an average as obtained from a global fit vs a two-step fit of partitioned datais used to illustrate that only in the case of a priori weighting do the results have the usually expected and desired statistical properties: normal distributions for residuals, t distributions for parameters assessed a posteriori, and x 2 distributions for variances.