Model Discrimination in Copolymerization Using the Sequential Bayesian Monte Carlo Method

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.

Discrimination of Chain Branching Models in Addition Diene Polymerizations

“…Masoumi et al [40,41] used a new approach to investigate model discrimination, based on the sequential Bayesian Monte Carlo model discrimination (SBMCMD) method. In a later work, Masoumi et al [42] applied SBMCMD in simulated copolymerization systems to compare its performance with the performances of other statistical discrimination methods already used in previous studies, as reported by Burke et al [19] The authors also used the Hsiang and Reilly [22] method to analyzed the same copolymerization systems and compared the obtained results with the ones presented in previous works. According to their results, the SBMCMD method could select the best model with fewer experiments.…”

Model Discrimination between RAFT Polymerization Models Using Sequential Bayesian Methodology

“…[6,7] A sequential Bayesian Monte Carlo model discrimination (SBMCMD) method was first introduced in Masoumi et al, [8] developed further in a second paper by Masoumi et al, [9] and used for discrimination between copolymerization models in a third paper from the same authors. [10] SBMCMD benefits from advantages of both being a sequential model discrimination method and using Markov Chain Monte Carlo (MCMC) techniques. This makes it a flexible method applicable to all types of models regardless of their structure (nested vs nonnested, or linear vs nonlinear).…”