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Keywords:

  • model discrimination;
  • marginal likelihood;
  • sequential experimental design;
  • Bayesian model selection

Abstract

In this paper a new approach to model discrimination is presented that takes advantage of Markov Chain Monte Carlo (MCMC) methods. It combines an experimental criterion first proposed by Roth (Roth, Design of Experiments for Discrimination Among rival Models, PhD, Thesis, Princeton University, New Jersey, USA, 1965) with an adaptation of a model selection method described by Chib and Jeliazkov [Chib and Jeliazkov, Stat. Neerl. 59, 30–44 (2005)], which uses an Acceptance–Rejection Metropolis–Hastings algorithm to evaluate the model marginal likelihood thus enabling the calculation of model posterior probabilities. It does so without requiring any linearisation of nonlinear models. In designing model discrimination experiments using the Roth criterion, MCMC methods are again used to find the mean of the predicted values by integrating over the entire parameter probability density function. The method is illustrated using the well-known chemical reaction kinetics example first discussed by Box and Hill [Box and Hill, Technometrics 9, 57–71 (1967)]. The results indicate that the method is very successful in identifying the correct model. Higher error levels and more complex kinetics require on average more model discrimination experiments. © 2012 Canadian Society for Chemical Engineering