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José Carlos Pinto - One of the best experts on this subject based on the ideXlab platform.
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Experimental design for the joint Model Discrimination and precise parameter estimation through information measures
Chemical Engineering Science, 2011Co-Authors: André L. Alberton, Marcio Schwaab, Marcos Wandir Nery Lobão, José Carlos PintoAbstract:Experimental design procedures for Model Discrimination and for estimation of precise Model parameters are usually treated as independent techniques. In order to conciliate the objectives of both experimental design procedures, the present paper proposes the use of experimental design criteria that are based on measures of the information gain when new experiments are carried out. The proposed criterion depends on the volumes of the confidence regions of the Model parameters and presents a number of advantageous aspects, such as the conciliation of the usual experimental design objectives and the fact that the obtained criterion values can be easily interpreted in terms of the information eliminated after carrying out additional experiments. Besides, the proposed design criterion can easily accommodate multiobjective experimental design approaches, as shown in the examples.
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Sequential experimental design for Model Discrimination: Taking into account the posterior covariance matrix of differences between Model predictions
Chemical Engineering Science, 2008Co-Authors: Marcio Schwaab, José Luiz Fontes Monteiro, José Carlos PintoAbstract:Techniques for experimental design of experiments for Model Discrimination constitute important tools for scientists and engineers, as analyzed phenomena can very often be described fairly well by different mathematical Models. As interpretation and use of available experimental data depend on the Model structure, techniques for design of experiments for selection of the best Model are of fundamental importance. Besides, experiments must often be designed for estimation of Model parameters and reduction of variances of Model predictions (or parameter estimates). These two classes of experimental design techniques generally lead to different experimental designs, although Model Discrimination and reduction of variances of parameter estimates are closely related to each other. In this work the posterior covariance matrix of difference between Model predictions is taken into account during the design for Model Discrimination for the first time. The obtained results show that the Model Discrimination power becomes much higher when the posterior covariance matrix of difference between Model predictions are considered during the experimental design, increasing the capability of Model Discrimination and simultaneously leading to improved parameter estimates.
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A new approach for sequential experimental design for Model Discrimination
Chemical Engineering Science, 2006Co-Authors: Marcio Schwaab, Fabricio M. Silva, Christian A. Queipo, Amaro Gomes Barreto, Márcio Nele, José Carlos PintoAbstract:Model Discrimination procedures are useful tools for selection of the best mathematical Models to be used to represent a specific chemical process. The present paper presents and discusses a new sequential Discrimination procedure, which makes use of Model probabilities and concentrates the efforts on Models with higher probabilities. Model probabilities are determined based on simple statistical arguments. Four numerical examples illustrate the application of the proposed Discrimination procedure. The obtained results indicate that the new procedure is able to discriminate kinetic Models with fewer experiments when compared to other procedures and also indicates when Model Discrimination is not possible and, thus, when the sequential design must be halted. Furthermore, the speed of the proposed Discrimination procedure can be controlled by tuning a design parameter which reflects the analyst's mood (confidence) towards the Discrimination problem and allows for increase or decrease of the number of experiments required for Model Discrimination during the sequential procedure.
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Experimental design for Model Discrimination of thermodynamic Models
Fluid Phase Equilibria, 1998Co-Authors: Cláudio Dariva, José Vladimir De Oliveira, José Carlos PintoAbstract:Abstract Traditionally, the screening of thermodynamic Models in phase equilibria is performed only after obtaining a full set of experimental points. The aim of this work is to show that sequential Model Discrimination procedures may be used successfully to discriminate among rival thermodynamic Models and thus, as a guide for more rational data collection. In order to do that, three different sequential experimental design procedures are implemented and used to Model the solid–gas equilibrium at high pressures. One of the procedures is based on the Tsallis Statistics and depends on an empirical parameter which measures the risk that the experimenter is resolved to take in the decision-making stage. This procedure has been extended here to include prediction errors. It is shown here that the use of any of the three sequential Discrimination procedures allow the selection of adequate Models and Model parameters with a significant reduction of the experimental effort. The Tsallis parameter is shown to exert a great influence upon the discarding of the Models and the sequence of experiments. The prediction error is shown to be of fundamental importance for the proper selection of the next experiment.
James Mcgree - One of the best experts on this subject based on the ideXlab platform.
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Developments of the total entropy utility function for the dual purpose of Model Discrimination and parameter estimation in Bayesian design
2017Co-Authors: James McgreeAbstract:The total entropy utility function is considered for the dual purpose of Bayesian design for Model Discrimination and parameter estimation. A sequential design setting is proposed where it is shown how to efficiently estimate the total entropy utility for a wide variety of data types. Utility estimation relies on forming particle approximations to a number of intractable integrals which is afforded by the use of the sequential Monte Carlo algorithm for Bayesian inference. A number of motivating examples are considered for demonstrating the performance of total entropy in comparison to utilities for Model Discrimination and parameter estimation. The results suggest that the total entropy utility selects designs which are efficient under both experimental goals with little compromise in achieving either goal. As such, the total entropy utility is advocated as a general utility for Bayesian design in the presence of Model uncertainty.
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Developments of the total entropy utility function for the dual purpose of Model Discrimination and parameter estimation in Bayesian design
Computational Statistics & Data Analysis, 2017Co-Authors: James McgreeAbstract:The total entropy utility function is considered for the dual purpose of Model Discrimination and parameter estimation in Bayesian design. A sequential design setting is considered where it is shown how to efficiently estimate the total entropy utility function in discrete data settings. Utility estimation relies on forming particle approximations to a number of intractable integrals which is afforded by the use of the sequential Monte Carlo algorithm for Bayesian inference. A number of motivating examples are considered for demonstrating the performance of total entropy in comparison to utilities for Model Discrimination and parameter estimation. The results suggest that the total entropy utility selects designs which are efficient under both experimental goals with little compromise in achieving either goal. As such, for the type of problems considered in this paper, the total entropy utility is advocated as a general utility for Bayesian design in the presence of Model uncertainty.
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A sequential Monte Carlo framework for adaptive Bayesian Model Discrimination designs using mutual information
The Contribution of Young Researchers to Bayesian Statistics, 2013Co-Authors: Christopher C. Drovandi, James Mcgree, Anthony N. PettittAbstract:In this paper we present a unified sequential Monte Carlo (SMC) framework for performing sequential experimental design for discriminating between a set of Models. The Model Discrimination utility that we advocate is fully Bayesian and based upon the mutual information. SMC provides a convenient way to estimate the mutual information. Our experience suggests that the approach works well on either a set of discrete or continuous Models and outperforms other Model Discrimination approaches.
Marcio Schwaab - One of the best experts on this subject based on the ideXlab platform.
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Experimental design for the joint Model Discrimination and precise parameter estimation through information measures
Chemical Engineering Science, 2011Co-Authors: André L. Alberton, Marcio Schwaab, Marcos Wandir Nery Lobão, José Carlos PintoAbstract:Experimental design procedures for Model Discrimination and for estimation of precise Model parameters are usually treated as independent techniques. In order to conciliate the objectives of both experimental design procedures, the present paper proposes the use of experimental design criteria that are based on measures of the information gain when new experiments are carried out. The proposed criterion depends on the volumes of the confidence regions of the Model parameters and presents a number of advantageous aspects, such as the conciliation of the usual experimental design objectives and the fact that the obtained criterion values can be easily interpreted in terms of the information eliminated after carrying out additional experiments. Besides, the proposed design criterion can easily accommodate multiobjective experimental design approaches, as shown in the examples.
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Sequential experimental design for Model Discrimination: Taking into account the posterior covariance matrix of differences between Model predictions
Chemical Engineering Science, 2008Co-Authors: Marcio Schwaab, José Luiz Fontes Monteiro, José Carlos PintoAbstract:Techniques for experimental design of experiments for Model Discrimination constitute important tools for scientists and engineers, as analyzed phenomena can very often be described fairly well by different mathematical Models. As interpretation and use of available experimental data depend on the Model structure, techniques for design of experiments for selection of the best Model are of fundamental importance. Besides, experiments must often be designed for estimation of Model parameters and reduction of variances of Model predictions (or parameter estimates). These two classes of experimental design techniques generally lead to different experimental designs, although Model Discrimination and reduction of variances of parameter estimates are closely related to each other. In this work the posterior covariance matrix of difference between Model predictions is taken into account during the design for Model Discrimination for the first time. The obtained results show that the Model Discrimination power becomes much higher when the posterior covariance matrix of difference between Model predictions are considered during the experimental design, increasing the capability of Model Discrimination and simultaneously leading to improved parameter estimates.
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A new approach for sequential experimental design for Model Discrimination
Chemical Engineering Science, 2006Co-Authors: Marcio Schwaab, Fabricio M. Silva, Christian A. Queipo, Amaro Gomes Barreto, Márcio Nele, José Carlos PintoAbstract:Model Discrimination procedures are useful tools for selection of the best mathematical Models to be used to represent a specific chemical process. The present paper presents and discusses a new sequential Discrimination procedure, which makes use of Model probabilities and concentrates the efforts on Models with higher probabilities. Model probabilities are determined based on simple statistical arguments. Four numerical examples illustrate the application of the proposed Discrimination procedure. The obtained results indicate that the new procedure is able to discriminate kinetic Models with fewer experiments when compared to other procedures and also indicates when Model Discrimination is not possible and, thus, when the sequential design must be halted. Furthermore, the speed of the proposed Discrimination procedure can be controlled by tuning a design parameter which reflects the analyst's mood (confidence) towards the Discrimination problem and allows for increase or decrease of the number of experiments required for Model Discrimination during the sequential procedure.
Alexander Penlidis - One of the best experts on this subject based on the ideXlab platform.
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Model Discrimination via Designed Experiments: Discriminating Between the Terminal and Penultimate Models on the Basis of Weight Average Chain Length
Polymer Reaction Engineering, 1999Co-Authors: Rejean Landry, Thomas A. Duever, Alexander PenlidisAbstract:ABSTRACTSimulations have been used to study the application of weight average chain length for discriminating between the terminal and the penultimate copolymerization Models. A brief description of the Model Discrimination method and of the copolymerization Models is given. The problem of parameter observability is discussed, showing that weight average chain length on its own leads to highly correlated parameter estimates. Combining weight average chain length with triad fractions on the other hand, yields a powerful combination of measurements for Model Discrimination. In the simulation studies the correct Model was selected in each of a variety of different scenarios used. Compared to using triad fractions alone, including weight average chain length has several advantages, notable among which is the ability to estimate radical reactivity ratios, s1, and s2, which are not observable from triad fraction data alone. Also, weight average chain length is more sensitive to changes in the rate of polymeriza...
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Model Discrimination via designed experiments : Discrimination between the terminal and penultimate Models based on rate data
Chemical Engineering Science, 1995Co-Authors: Annette L. Burke, Thomas A. Duever, Alexander PenlidisAbstract:Abstract Simulations have been used to study the application of Model Discrimination methods to the problem of discriminating between the terminal and penultimate copolymerization Models on the basis of composition and rate data. Both Models are reviewed and the three Model Discrimination methods chosen for study are explained. Composition data have been used in conjunction with rate data due to the high correlation between estimated parameters based solely on rate data. This correlation has been discussed. The simulation programs are then explained including the generation of simulated data. Data are presented to show that the simulation programs can duplicate the experimental observations of other researchers. The results show that both the modified Buzzi-Ferraris method and the exact entropy method are able to correctly discriminate between the Models in greater than 95% of the simulations. Differences between the three Model Discrimination methods are discussed along with differences between the three copolymer measurements that have been studied.
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Model Discrimination via designed experiments: discriminating between the terminal and penultimate Models based on triad fraction data
Macromolecular Theory and Simulations, 1994Co-Authors: Annette L. Burke, Thomas A. Duever, Alexander PenlidisAbstract:Computer simulations have been used to study the application of statistical Model Discrimination techniques to the Modelling of copolymerization reactions based on triad fraction data. Since there are six triad fraction measurements, the problems of parameter estimation and Model Discrimination become multivariate problems. The multivariate forms of three Model Discrimination methods (exact entropy, Hsiang and Reilly, and Buzzi-Ferraris et al.) are presented. Programs have been developed to simulate the application of these techniques to the systems styrene-acrylonitrile, styrene-methyl methacrylate and styrene-butyl acrylate. The simulation programs are explained, including the method used to simulate triad fraction data. Evidence is presented that the simulation programs are capable of duplicating the type of measurements that would be obtained in the laboratory. The simulation results show that Model Discrimination methods are able to accurately and reliably discriminate between the terminal and penultimate Models. The use of simulated Model Discrimination methods leads to reliable Discrimination in fewer experiments than have been used in past work. Also, Model Discrimination methods are able to detect smaller penultimate effects than those found by Hill et al. for styrene-acrylonitrile. In addition, the results show that the use of four of the six triad fractions, versus one copolymer composition measurement, should lead to more precise reactivity ratio estimates and an increased ability to discriminate between the terminal and penultimate Models. Our work suggests that use of Model Discrimination methods will indeed lead to improvements in the Modelling of copolymerization reactions.
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Model Discrimination via designed experiments : discriminating between the terminal and penultimate Models on the basis of composition data
Macromolecules, 1994Co-Authors: Annette L. Burke, Thomas A. Duever, Alexander PenlidisAbstract:Computer simulations have been used to study the application of statistical Model Discrimination methods to the Modeling of copolymerizations. Statistical Model Discrimination methods describe how experiments should be designed and analyzed to obtain the maximum possible information on the strengths of competing Models. The potential benefits of applying Model Discrimination methods are described by contrasting them with pest work on the Modeling of copolymerizations. Three Model Discrimination techniques (Buzzi-Fenaris and Forzetti, 15 effect entropy, 14 and Hsiang end Reilly 21 ) have been applied to the systems styrene-acrylonitrile, styrene-methyl methacrylate, and styrene-butyl acrylate
Annette L. Burke - One of the best experts on this subject based on the ideXlab platform.
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Model Discrimination via designed experiments : Discrimination between the terminal and penultimate Models based on rate data
Chemical Engineering Science, 1995Co-Authors: Annette L. Burke, Thomas A. Duever, Alexander PenlidisAbstract:Abstract Simulations have been used to study the application of Model Discrimination methods to the problem of discriminating between the terminal and penultimate copolymerization Models on the basis of composition and rate data. Both Models are reviewed and the three Model Discrimination methods chosen for study are explained. Composition data have been used in conjunction with rate data due to the high correlation between estimated parameters based solely on rate data. This correlation has been discussed. The simulation programs are then explained including the generation of simulated data. Data are presented to show that the simulation programs can duplicate the experimental observations of other researchers. The results show that both the modified Buzzi-Ferraris method and the exact entropy method are able to correctly discriminate between the Models in greater than 95% of the simulations. Differences between the three Model Discrimination methods are discussed along with differences between the three copolymer measurements that have been studied.
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Model Discrimination via designed experiments: discriminating between the terminal and penultimate Models based on triad fraction data
Macromolecular Theory and Simulations, 1994Co-Authors: Annette L. Burke, Thomas A. Duever, Alexander PenlidisAbstract:Computer simulations have been used to study the application of statistical Model Discrimination techniques to the Modelling of copolymerization reactions based on triad fraction data. Since there are six triad fraction measurements, the problems of parameter estimation and Model Discrimination become multivariate problems. The multivariate forms of three Model Discrimination methods (exact entropy, Hsiang and Reilly, and Buzzi-Ferraris et al.) are presented. Programs have been developed to simulate the application of these techniques to the systems styrene-acrylonitrile, styrene-methyl methacrylate and styrene-butyl acrylate. The simulation programs are explained, including the method used to simulate triad fraction data. Evidence is presented that the simulation programs are capable of duplicating the type of measurements that would be obtained in the laboratory. The simulation results show that Model Discrimination methods are able to accurately and reliably discriminate between the terminal and penultimate Models. The use of simulated Model Discrimination methods leads to reliable Discrimination in fewer experiments than have been used in past work. Also, Model Discrimination methods are able to detect smaller penultimate effects than those found by Hill et al. for styrene-acrylonitrile. In addition, the results show that the use of four of the six triad fractions, versus one copolymer composition measurement, should lead to more precise reactivity ratio estimates and an increased ability to discriminate between the terminal and penultimate Models. Our work suggests that use of Model Discrimination methods will indeed lead to improvements in the Modelling of copolymerization reactions.
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Model Discrimination via designed experiments : discriminating between the terminal and penultimate Models on the basis of composition data
Macromolecules, 1994Co-Authors: Annette L. Burke, Thomas A. Duever, Alexander PenlidisAbstract:Computer simulations have been used to study the application of statistical Model Discrimination methods to the Modeling of copolymerizations. Statistical Model Discrimination methods describe how experiments should be designed and analyzed to obtain the maximum possible information on the strengths of competing Models. The potential benefits of applying Model Discrimination methods are described by contrasting them with pest work on the Modeling of copolymerizations. Three Model Discrimination techniques (Buzzi-Fenaris and Forzetti, 15 effect entropy, 14 and Hsiang end Reilly 21 ) have been applied to the systems styrene-acrylonitrile, styrene-methyl methacrylate, and styrene-butyl acrylate