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Combining Statistical Methods and Fu...

Gibson, Lauren,

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Combining Statistical Methods and Fundamental Models for Polymerization and Pharmaceutical Processes /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Combining Statistical Methods and Fundamental Models for Polymerization and Pharmaceutical Processes // Lauren Gibson.
作者:	Gibson, Lauren,
面頁冊數:	1 electronic resource (372 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-04, Section: B.
Contained By:	Dissertations Abstracts International86-04B.
標題:	Polymers. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31580777
ISBN:	9798342137805

Combining Statistical Methods and Fundamental Models for Polymerization and Pharmaceutical Processes /
Gibson, Lauren,

Combining Statistical Methods and Fundamental Models for Polymerization and Pharmaceutical Processes /Lauren Gibson. - 1 electronic resource (372 pages)

Source: Dissertations Abstracts International, Volume: 86-04, Section: B.

Fundamental models and statistical methods are developed and applied for polymerization and pharmaceutical processes. First, two fundamental models for gas-phase ethylene/hexene copolymerization with a three-site metallocene catalyst are developed. The first model predicts the joint molecular weight and copolymer composition distribution for lab-scale copolymerization at temperatures between 60 and 85 oC. The second model predicts product properties obtained during continuous pilot-plant operation. Both polymerization models have many unknown rate constants and activation energies. Although large data sets are available for parameter estimation, only subsets of the model parameters (i.e., 53 out of 60 in the first modeling study and 34 out of 61 in the second) can be reliably estimated to avoid overfitting the data.The second half of this thesis focuses on new Bayesian statistical methods that make it possible to estimate all of the model parameters using limited data. In the first statistical-method project, a new objective function for D-optimal model-based design of experiments (MBDoE) is derived and used to select experimental conditions for a pharmaceutical case study with a singular Fisher information matrix (FIM). This Bayesian objective function accounts for prior information about plausible values of the model parameters, resulting in an invertible augmented FIM. A minimum volume ellipsoid (MVE) methodology is proposed for comparing the effectiveness of designed experiments. Testing the proposed MBDoE method using MVEs confirms that the proposed D-optimal objective function leads to reliable parameter estimates that tend to occupy smaller ellipsoids than estimates from A-optimal experiments.The second statistical-method project is concerned with Bayesian methods for estimating parameters in fundamental models of chemical processes. Simple objective functions are derived for situations involving truncated normal priors or uniform priors for model parameters. These types of priors are attractive because they are more consistent with hard parameter bounds enforced during parameter estimation than unbounded normal priors are. A new parametric bootstrapping approach that considers model nonlinearity and truncated normal priors is proposed to obtain information about uncertainties associated with estimated parameters. A pharmaceutical case study is used to illustrate the effectiveness of the proposed objective functions and bootstrapping method.

English

ISBN: 9798342137805Subjects--Topical Terms:

535398
Polymers.

Combining Statistical Methods and Fundamental Models for Polymerization and Pharmaceutical Processes /
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520 $a Fundamental models and statistical methods are developed and applied for polymerization and pharmaceutical processes. First, two fundamental models for gas-phase ethylene/hexene copolymerization with a three-site metallocene catalyst are developed. The first model predicts the joint molecular weight and copolymer composition distribution for lab-scale copolymerization at temperatures between 60 and 85 oC. The second model predicts product properties obtained during continuous pilot-plant operation. Both polymerization models have many unknown rate constants and activation energies. Although large data sets are available for parameter estimation, only subsets of the model parameters (i.e., 53 out of 60 in the first modeling study and 34 out of 61 in the second) can be reliably estimated to avoid overfitting the data.The second half of this thesis focuses on new Bayesian statistical methods that make it possible to estimate all of the model parameters using limited data. In the first statistical-method project, a new objective function for D-optimal model-based design of experiments (MBDoE) is derived and used to select experimental conditions for a pharmaceutical case study with a singular Fisher information matrix (FIM). This Bayesian objective function accounts for prior information about plausible values of the model parameters, resulting in an invertible augmented FIM. A minimum volume ellipsoid (MVE) methodology is proposed for comparing the effectiveness of designed experiments. Testing the proposed MBDoE method using MVEs confirms that the proposed D-optimal objective function leads to reliable parameter estimates that tend to occupy smaller ellipsoids than estimates from A-optimal experiments.The second statistical-method project is concerned with Bayesian methods for estimating parameters in fundamental models of chemical processes. Simple objective functions are derived for situations involving truncated normal priors or uniform priors for model parameters. These types of priors are attractive because they are more consistent with hard parameter bounds enforced during parameter estimation than unbounded normal priors are. A new parametric bootstrapping approach that considers model nonlinearity and truncated normal priors is proposed to obtain information about uncertainties associated with estimated parameters. A pharmaceutical case study is used to illustrate the effectiveness of the proposed objective functions and bootstrapping method.
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