A Posterior Predictive Approach to Multiple Response Surface Optimization

Peterson, John J.

doi:10.1080/00224065.2004.11980261

Cited by 120 publications

(80 citation statements)

References 19 publications

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“…The regression models were attained (Table 4) from the results obtained to the proposed design (Table 3) in function of the number of elements per axis Deviation relative to experimental data for NaCl and KCl were highly correlated (r=0.98), and therefore the use of only one of these dependent variables is recommended in the simultaneous optimization (Peterson, 2004). Thus, when one is minimized the other one will consequently be minimized as well.…”

Section: Results and Results And Results Andmentioning

confidence: 99%

Otimização da discretização espaço-temporal do método de elementos finitos aplicado a simulação da difusão multicomponente

et al. 2006

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ABSTRACT. The space and time discretization of the finite element method was optimized for following application in multicomponent diffusion simulation during Prato cheese salting, a traditional and much consumed foodstuff in Brazil originated from the European Gouda cheese. It was ascertained that the correct choice of the time intervals and mesh is fundamental in applying the method. After optimization the simulated results were in agreement with the experimental and calculated results by the analytical method, showing that the method is a promising tool for simulation of diffusive processes when two solutes are considered, and is also a much less restrictive technique than the analytical method.Key words: response surface methodology, simplex optimization, desirability functions, prato cheese salting.RESUMO. Otimização da discretização espaço-temporal do método de elementos finitos aplicado a simulação da difusão multicomponente. Neste trabalho foi realizada a otimização da discretização espaço-temporal do método de elementos finitos para sua posterior aplicação na simulação da difusão multicomponente durante a salda de queijo prato, um alimento tradicional e muito consumido no Brasil e similar ao queijo Gouda. Foi verificado que a escolha correta dos intervalos de tempo e da malha é fundamental para a aplicação do método. Após a otimização os resultados simulados concordaram com os experimentais e estimados pelo método analítico. Mostrando que o método é uma ferramenta promissora para a simulação de processos difusivos quando dois solutos são considerados, além de ser uma técnica muito menos restritiva que o método analítico.Palavras-chave: metodologia de superfície de respostas, otimização simplex, funções de desejabilidade, salga de queijo prato.

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Section: Results and Results And Results Andmentioning

confidence: 99%

Otimização da discretização espaço-temporal do método de elementos finitos aplicado a simulação da difusão multicomponente

et al. 2006

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“…En el presente trabajo se utiliza un enfoque bayesiano propuesto por Peterson (2004), en el que también se considera la probabilidad de que el proceso cumpla con los requisitos de calidad de las características del producto a optimizar consideradas en el análisis y toma en cuenta la estructura de correlación y la incertidumbre en los parámetros de los modelos. Miro-Quesada et al (2004), mencionan que el problema de la optimización de respuestas múltiples consiste en escoger los valores de los k factores controlables x i , tal que el vector de respuestas y tenga ciertas propiedades deseadas.…”

Section: El Enfoque Bayesiano Para Optimización De Respuestas Múltiplesunclassified

“…Según Peterson (2004), debido a que la ecuación (5), sigue una distribución t multivariada, es fácil simular valores para y de esta densidad predictiva. Johnson (1987) en su libro Multivariate statistical simulation menciona que se puede simular una variable aleatoria t -variada y, mediante la simulación de una variable aleatoria normal multivariada y una variable aleatoria chi-cuadrada independiente (Peterson, 2004).…”

Section: El Enfoque Bayesiano Para Optimización De Respuestas Múltiplesunclassified

“…Según Ames et al, (1997), al minimizar la función de pérdida además de la calidad más alta, también se produce la mayor estabilidad o robustez en el proceso contra las variaciones en la calidad debida a las variables de entrada. Peterson (2004) menciona que actualmente existen enfoques basados en la función cuadrática de pérdida que consideran la estructura de correlaciones entre los diferentes tipos de respuestas, sin embargo, también menciona que esta técnica tiene dos inconvenientes serios, primero, no considera la incertidumbre de la matriz de varianzas-covarianzas de los errores en los modelos de regresión y segundo, en algunas ocasiones la función cuadrática de pérdida, especialmente alguna que se base en una forma cuadrática multivariada puede ser difícil de entender para algunos investigadores.…”

Section: Introductionunclassified

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Metodología bayesiana para la optimización simultánea de múltiples respuestas

Limón¹,

Rodríguez²,

Sánchez³

et al. 2012

Inf. tecnol.

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ResumenSe muestra la aplicación de una metodología bayesiana para la optimización simultánea de múltiples respuestas. Se modifica una propuesta anterior, introduciendo una modificación que la hace más flexible, ya que permite trabajar con el caso en que no todas las variables consideradas en el estudio son igualmente importantes. Para incorporar estas diferencias en cuanto a la relevancia de las variables de respuesta analizadas se utiliza la media geométrica ponderada de las probabilidades de que cada variable cumpla con su especificación. Con esto, las múltiples variables a optimizar se convierten en una sola. Mediante un ejemplo se muestra como la modificación propuesta ayuda a obtener distintos escenarios óptimos para considerar en la toma de decisiones. Palabras clave: múltiples respuestas, optimización, metodología bayesiana, media geométrica ponderada Bayesian methodology for simultaneous optimization of multiple responses AbstractThe application of a bayesian methodology for simultaneous optimization of multiple responses is presented. A previous proposal is modified by introducing a modification that makes it more flexible, allowing working with the case in which not all the variables considered in the study are equally important. To incorporate in the methodology these differences related to the analyzed response variables the weighted geometric mean of the probabilities that each variable meets its own specification is used. With this change, the multiple optimization variables are converted into only one. An example to show how the proposed modification helps in achieving different optimal scenarios to consider in making decisions is discussed.

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“…The key statistical challenges to overcome to make QbD a reality for such longitudinal data are critical: It can be postulated that a Bayesian approach is the only option to practically achieve such an objective as required by ICH-Q8. The justification and added value of the use of Bayesian statistics for proper QbD implementation has been discussed extensively by several authors such as Peterson et al [13][14][15][16][17], Miró-Quesada [12] and Lebrun et al [11].…”

Section: Introductionmentioning

confidence: 99%

A Quality By Design Approach For Longitudinal Quality Attributes

Lebrun

Giacoletti²,

Scherder³

et al. 2014

Journal of Biopharmaceutical Statistics

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The concept of Quality by Design (QbD) as published in ICH-Q8 is currently one of the most recurrent topics in the pharmaceutical literature. This guideline recommends the use of information and prior knowledge gathered during pharmaceutical development studies to provide a scientific rationale for the manufacturing process of a product and provide guarantee of future quality. This poses several challenges from a statistical standpoint and requires a shift in paradigm from traditional statistical practices. First, to provide "assurance of quality" of future lots implies the need to make predictions regarding quality given past evidence and data. Second, the Quality Attributes described in the Q8 guidelines are not always a set of unique, independent measurements. In many cases, these criteria are complicated longitudinal data with successive acceptance criteria over a defined period of time. A common example is a dissolution profile for a modified or extended release solid dosage form that must fall within acceptance limits at several time points. A Bayesian approach for longitudinal data obtained in various conditions of a Design of Experiment is provided to elegantly address the ICH-Q8 recommendation to provide assurance of quality and derive a scientifically sound Design Space.

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A Posterior Predictive Approach to Multiple Response Surface Optimization

Cited by 120 publications

References 19 publications

Otimização da discretização espaço-temporal do método de elementos finitos aplicado a simulação da difusão multicomponente

Otimização da discretização espaço-temporal do método de elementos finitos aplicado a simulação da difusão multicomponente

Metodología bayesiana para la optimización simultánea de múltiples respuestas

A Quality By Design Approach For Longitudinal Quality Attributes

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