Statistics for Environmental Engineers

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A Model Discrimination Function


A statistical method for model discrimination based on calculating the posterior probability in favor of each model being correct has been proposed (Box and Hill, 1967). This criterion should not be allowed to select a correct model, but it may be used to eliminate one or more models as being unworthy of additional investigation.


Posterior probability is the probability computed after the models have been fitted to the data. Before the models are fitted, we may have no particular reason to favor one model over another; that is, each model


is equally likely to be correct. Therefore we say that the prior probabilities are equal for the four models. This means that, before we fit any of the models, we give them equal standing on scientific grounds and are willing to accept any one of them that fits the available data.


The criterion to be used assumes that the residual sums of squares of the rival models can be used to discriminate, with the better models having the lower RSS values. The posterior probability that each model is the best is calculated as a function of the RSS, adjusted for the number of parameters in the model.

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