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Model discrimination and criticism with single‐response data
Author(s) -
Stewart Warren E.,
Henson Thomas L.,
Box George E. P.
Publication year - 1996
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690421107
Subject(s) - bayes' theorem , statistics , mathematics , variance (accounting) , goodness of fit , inverse , criticism , set (abstract data type) , sampling (signal processing) , bayesian probability , data set , bayes factor , econometrics , algorithm , computer science , geometry , art , accounting , literature , filter (signal processing) , business , computer vision , programming language
The inverse probability theorem of Bayes is used, along with sampling theory, to obtain objective criteria for choosing among rival models. Formulas are given for the relative posterior probabilities of candidate models and for their goodness of fit, when the models are fitted to a common data set with Normally distributed errors. Cases of full, partial and minimal variance information are treated. The formulas are demonstrated with three examples, including a kinetic study of a catalytic reaction.