Optimal designs for nonlinear regression models with respect to non-informative priors

Burghaus, Ina; Dette, Holger

doi:10.1016/j.jspi.2014.05.009

Cited by 14 publications

(7 citation statements)

References 43 publications

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“…Nonlinear regression models describe the relationship between a response and a predictor (Burghaus & Dette, 2014). In microbiology studies, mathematical models are used to describe the behavior of microorganisms under different physical and chemical conditions (Zwietering, de Koos, Hasenack, de Witt, & van't Riet, 1991).…”

Section: (4)mentioning

confidence: 99%

Effect of temperature-time on sterilization process for a jacketed bioreactor system: Application of a Ratkowsky Nonlinear Model

Montero-Zamora¹

2018

Ingeniería

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Steam sterilization is a technique widely implemented in different biotechnological processes-among them the growth of microorganisms in bioreactors-, which require initial aseptic conditions. In the present research, the relationship between lethality and death rate of Bacillus cereus grown in 7-liter stirred-tank jacketed bioreactors was investigated, with sugar cane molasses as a carbon source. The sterilization process was tested with an industrial autoclave within data loggers in bioreactors, which measure the temperature in the cold point to quantify the accumulated lethality. Through data analysis, a contour plot allows a graphical prediction of the microbiological sterilization results in terms of colony forming units (CFU).

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Section: (4)mentioning

confidence: 99%

Effect of temperature-time on sterilization process for a jacketed bioreactor system: Application of a Ratkowsky Nonlinear Model

Montero-Zamora¹

2018

Ingeniería

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“…Optimal design for generalized linear models (GLMs) (Khuri et al, 2006;Fedorov and Leonov, 2013) is an important topic in the design of experiments area. In recent years, there have been new developments on both theoretical and algorithmic fronts, such as Woods and Lewis (2011); Yang et al (2011); Burghaus and Dette (2014); Wu and Stufken (2014); Wong et al (2019) among many others. A key challenge of optimal design for GLMs is that the design criterion often depends on the regression model assumption, including the specification of the link function, the linear predictor, and the values of the unknown regression coefficients.…”

Section: Introductionmentioning

confidence: 99%

A Maximin Φp-Efficient Design for Multivariate Generalized Linear Models

Li¹,

Kang²,

Deng³

2023

STAT SINICA

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Experimental designs for a generalized linear model (GLM) often depend on the specification of the model, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with the uncertainties of these model specifications, it is important to construct optimal designs with high efficiency under such uncertainties. Existing methods such as Bayesian experimental designs often use prior distributions of model specifications to incorporate model uncertainties into the design criterion. Alternatively, one can obtain the design by optimizing the worst-case design efficiency with respect to the uncertainties of model specifications. In this work, we propose a new Maximin Φp-Efficient (or Mm-Φp for short) design which aims at maximizing the minimum Φp-efficiency under model uncertainties. Based on the theoretical properties of the proposed criterion, we develop an efficient algorithm with sound convergence properties to construct the Mm-Φp design. The performance of the proposed Mm-Φp design is assessed through several numerical examples.

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“…Optimal design for generalized linear models (GLMs) (Sitter and Torsney, 1995;Khuri et al, 2006;Silvey, 2013;Fedorov and Leonov, 2013) is an important topic in the design of experiments area. In recent years, there have been new developments on both theoretical and algorithmic fronts, such as Woods and Lewis (2011); Yang et al (2011); Burghaus and Dette (2014); Wu and Stufken (2014); Waite and Woods (2015); Wong et al (2019) among many others. A key challenge of optimal design for GLMs is that the design criterion often depends on the regression model assumption, including the specification of the link function, the linear predictor and the values of the unknown regression coefficients.…”

Section: Introductionmentioning

confidence: 99%

A Maximin $Φ_{p}$-Efficient Design for Multivariate GLM

Li,

Kang,

Deng

2020

Preprint

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Experimental designs for a generalized linear model (GLM) often depend on the specification of the model, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with uncertainties of these model specifications, it is important to construct optimal designs with high efficiency under such uncertainties. Existing methods such as Bayesian experimental designs often use prior distributions of model specifications to incorporate model uncertainties into the design criterion. Alternatively, one can obtain the design by optimizing the worst-case design efficiency with respect to uncertainties of model specifications. In this work, we propose a new Maximin Φp-Efficient (or Mm-Φp for short) design which aims at maximizing the minimum Φp-efficiency under model uncertainties. Based on the theoretical properties of the proposed criterion, we develop an efficient algorithm with sound convergence properties to construct the Mm-Φp design. The performance of the proposed Mm-Φp design is assessed through several numerical examples.

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Optimal designs for nonlinear regression models with respect to non-informative priors

Cited by 14 publications

References 43 publications

Effect of temperature-time on sterilization process for a jacketed bioreactor system: Application of a Ratkowsky Nonlinear Model

Effect of temperature-time on sterilization process for a jacketed bioreactor system: Application of a Ratkowsky Nonlinear Model

A Maximin Φp-Efficient Design for Multivariate Generalized Linear Models

A Maximin $Φ_{p}$-Efficient Design for Multivariate GLM

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