Model Discrimination and Criticism with Single-Response Data

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 (Example 1 treats linear models for data with a given variance; Example 2 treats a pair of nonlinear models, using a variance estimated by replication; and Example 3 treats a set of eighteen nonlinear models, using a variance estimated from residuals of a higher-order model (a kinetic study of hydrogenation of mixed isooctenes over a supported nickel catalyst))

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