Discrimination Among Mechanistic Models

Box, George E. P.; Hill, William J.

doi:10.1080/00401706.1967.10490441

Cited by 349 publications

(230 citation statements)

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“…The efficiency of such experiments depends on their design which in turn depends on the criterion used to assess whether or not discrimination has been achieved. A sequential experiment design strategy for distinguishing among mechanistic models has been reported (Box and Hill, 1967) and applied by Hunter and Mezaki (1967). This strategy aims to maximize the change in entropy at each stage of the experiment and assess model discrimination by comparing the Bayesian posterior probabilities of the models being considered.…”

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confidence: 99%

“…This strategy aims to maximize the change in entropy at each stage of the experiment and assess model discrimination by comparing the Bayesian posterior probabilities of the models being considered. However, neither Box and Hill (1967) nor Hunter and Mezaki (1967) stated explicitly how they computed the model posterior probabilities nor did they discuss their assumptions regarding the prior probability densities of the parameters of the models. Reilly (1970) and Atkinson (1978) considered the use of proper priors for the parameters of the models whereas Box and Hill (1967) appear to have used improper priors (Atkinson and Cox, 1974).…”

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confidence: 99%

“…However, neither Box and Hill (1967) nor Hunter and Mezaki (1967) stated explicitly how they computed the model posterior probabilities nor did they discuss their assumptions regarding the prior probability densities of the parameters of the models. Reilly (1970) and Atkinson (1978) considered the use of proper priors for the parameters of the models whereas Box and Hill (1967) appear to have used improper priors (Atkinson and Cox, 1974). In their original report Box and Hill (1967) demonstrated effective discrimination even when certain models are specific cases of other models.…”

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confidence: 99%

“…Reilly (1970) and Atkinson (1978) considered the use of proper priors for the parameters of the models whereas Box and Hill (1967) appear to have used improper priors (Atkinson and Cox, 1974). In their original report Box and Hill (1967) demonstrated effective discrimination even when certain models are specific cases of other models. We believe that this property may lead to the posterior probabilities being biased in favour of one or more of the models being considered.…”

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confidence: 99%

“…The existence of such bias depends on the assumptions made regarding the prior probability densities of the model parameters. Furthermore, Box and Hill (1967) addressed a restricted situation by assuming that the variance of the experimental error is known to the experimenter and is homoscedastic.…”

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confidence: 99%

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Model discrimination: Posterior probabilities

Dunne

Lacey

1984

Can J Chem Eng

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Expressions were derived for the computation of regression model posterior probabilities under a number of assumptions regarding the form of the uniform parameter prior probability density function. It was demonstrated that some of these forms may lead to a bias in the model posterior probabilities. The variance known and unknown situations were considered under both homoscedastic and heteroscedastic conditions. Bias of the model posterior probabilities may partly explain the unstable behaviour reported by previous workers.

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confidence: 99%