No 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

The use of sequential Bayesian methodology for model discrimination purposes in reversible addition‐fragmentation transfer (RAFT) polymerization is analyzed and discussed from a mathematical model discrimination point of view. The RAFT models are detailed nonlinear mechanistic models from the literature, where the debate is still ongoing about their validity. A sensitivity analysis is performed first on the simulated models in order to identify the most informative process (measured) outputs from the candidate models with respect to model discrimination. Next, sequential Bayesian Monte Carlo model discrimination (SBMCMD) methodology is applied to discriminate between the two rival models. The effectiveness of the SBMCMD procedure in discriminating between the two proposed models (both describing basic RAFT polymerization kinetic trends successfully) is explored further. Most informative experiments are designed and suggested based on the design of experiments step of the SBMCMD methodology. The methodology is capable of selecting the “real” model.

No abstract

The term model discrimination, as used in this paper, refers to the sequential process of designing experi mental conditions, carrying out the new experiment and analyzing competitive models. Experiments are designed in these procedures to provide the maximum possible information from the minimum number of experiments with respect to discrimination between the rival models.Burke et al. [1][2][3][4] studied the application of statistical model discrimination methods to terminal and penultimate copoly merization models. They applied three different model dis crimination methods, including exact entropy (EE), [5] Hsiang and Reilly (HR), [6] and BuzziFerraris and Forzatti (BFF) Methods, [7][8][9] to three different copolymer systems, namely styrene and methyl methacrylate (STY/MMA), styrene acry lonitrile (STY/AN), styrene and butyl acrylate (STY/BA), in order to find the best discrimination method and the best measurement or combination of measurements to discrim inate between copolymerization models.Here, the sequential Bayesian Monte Carlo model dis crimination (SBMCMD) [10,11] method will be applied toThe authors have introduced and extended the sequential Bayesian Monte Carlo model dis crimination (SBMCMD) method described in previous studies by Masoumi et al. for the pur pose of discriminating between mechanistic models via designed experiments. The features of the Markov Chain Monte Carlo methods utilized in SBMCMD allow this method to work with a wide range of nonlinear models. Here, SBMCMD has been applied to simulated copoly merization systems to compare its performance with other statistical discrimination methods used in previous studies by Burke et al. In addition, the Hsiang and Reilly method has been reapplied to the same copolymerization systems to address questions arising from previous work on this subject. The results of applying the SBMCMD method show that it is possible to choose the best model cor rectly with fewer experiments compared to the previously studied methods. Results also confirm that copolymer com position data do not provide enough information to discrimi nate between terminal and penultimate data.