Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model
In practice, complications can arise when constructing optimal designs for non-linear regression models. One of the major problems is when the observations are correlated, since they are taken from the same individual, object or experimental unit. When using the D-optimality criterion, it depends bo...
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2019
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| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/9504 |
| _version_ | 1801706345233121280 |
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| author | Mosquera Benítez, Juan Carlos López Rios, Victor Ignacio |
| author_facet | Mosquera Benítez, Juan Carlos López Rios, Victor Ignacio |
| author_sort | Mosquera Benítez, Juan Carlos |
| collection | OJS |
| description | In practice, complications can arise when constructing optimal designs for non-linear regression models. One of the major problems is when the observations are correlated, since they are taken from the same individual, object or experimental unit. When using the D-optimality criterion, it depends both on the parameter vector of the model and on the correlation structure assumed for the error term. One way to avoid this dependence is through the inclusion of a priori distributions in the D-optimality criterion. In this paper we study the effect of the choice of different a priori distributions, such as the Uniform, Gamma and Lognormal distributions in obtaining the D-optimal designs for a non-linear model, when the errors present different correlation structures. The designs are found by maximizing the approximate D-optimality criterion by the Monte Carlo method. In addition, a general methodology is proposed to find D-optimal designs for any type of non-linear model in the presence of correlated observations. Finally, it is proposed to compare the designs found by calculating the efficiencies taking as a reference design the one obtained with the a priori Uniform distribution. The methodology established in a case study is applied, and it is concluded that the designs obtained depend as much on the correlation structure as on the a priori distribution considered. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-9504 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2019 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-95042020-11-11T02:06:38Z Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model Efecto de distribuciones a priori en los diseños D-óptimos Bayesianos para un modelo no lineal correlacionado Mosquera Benítez, Juan Carlos López Rios, Victor Ignacio Diseño D-óptimo, Modelos no lineales, Estructura de correlación, Matriz de Información de Fisher, Distribuciones a priori D-optimal design, non-linear models, correlation structure, Fisher Information Matrix, a priori distributions In practice, complications can arise when constructing optimal designs for non-linear regression models. One of the major problems is when the observations are correlated, since they are taken from the same individual, object or experimental unit. When using the D-optimality criterion, it depends both on the parameter vector of the model and on the correlation structure assumed for the error term. One way to avoid this dependence is through the inclusion of a priori distributions in the D-optimality criterion. In this paper we study the effect of the choice of different a priori distributions, such as the Uniform, Gamma and Lognormal distributions in obtaining the D-optimal designs for a non-linear model, when the errors present different correlation structures. The designs are found by maximizing the approximate D-optimality criterion by the Monte Carlo method. In addition, a general methodology is proposed to find D-optimal designs for any type of non-linear model in the presence of correlated observations. Finally, it is proposed to compare the designs found by calculating the efficiencies taking as a reference design the one obtained with the a priori Uniform distribution. The methodology established in a case study is applied, and it is concluded that the designs obtained depend as much on the correlation structure as on the a priori distribution considered. En la práctica pueden surgir complicaciones a la hora de construir diseños óptimos para modelos de regresión no lineales, uno de los grandes problemas se evidencia cuando las observaciones son correlacionadas, debido a que éstas son tomadas de un mismo individuo, objeto o unidad experimental. Al momento de utilizar el criterio de D-optimalidad este depende tanto del vector de parámetros del modelo como de la estructura de correlación supuesta para el término de error. Una forma de evitar esta dependencia es mediante la inclusión de distribuciones a priori en el criterio de D-optimalidad. En este artículo se estudia el efecto que tiene la escogencia de diferentes distribuciones a priori, tales como las distribuciones Uniforme, Gamma y Log normal en la obtención de los diseños D-óptimos para un modelo no lineal, cuando los errores presentan diferentes estructuras de correlación. Se hallan los diseños al maximizar el criterio de D-optimalidad aproximado por el método de Monte Carlo. Además, se propone una metodología general que permite hallar diseños D-óptimos para cualquier tipo de modelo no lineal en presencia de observaciones correlacionadas. Finalmente, se propone comparar los diseños encontrados mediante el cálculo de las eficiencias tomando como diseño de referencia el obtenido con la distribución a priori Uniforme. Se aplica la metodología establecida en un caso de estudio, y se concluye que los diseños obtenidos dependen tanto de la estructura de correlacióncomo de la distribución a priori considerada. Universidad Pedagógica y Tecnológica de Colombia 2019-07-23 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/9504 10.19053/01217488.v10.n2.2019.9504 Ciencia En Desarrollo; Vol. 10 No. 2 (2019): Vol 10, Núm. 2 (2019): Julio - Diciembre; 165-179 Ciencia en Desarrollo; Vol. 10 Núm. 2 (2019): Vol 10, Núm. 2 (2019): Julio - Diciembre; 165-179 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/9504/8671 |
| spellingShingle | Diseño D-óptimo, Modelos no lineales, Estructura de correlación, Matriz de Información de Fisher, Distribuciones a priori D-optimal design, non-linear models, correlation structure, Fisher Information Matrix, a priori distributions Mosquera Benítez, Juan Carlos López Rios, Victor Ignacio Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model |
| title | Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model |
| title_alt | Efecto de distribuciones a priori en los diseños D-óptimos Bayesianos para un modelo no lineal correlacionado |
| title_full | Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model |
| title_fullStr | Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model |
| title_full_unstemmed | Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model |
| title_short | Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model |
| title_sort | effect of a priori distributions in bayesian d optimal designs for a correlated non linear model |
| topic | Diseño D-óptimo, Modelos no lineales, Estructura de correlación, Matriz de Información de Fisher, Distribuciones a priori D-optimal design, non-linear models, correlation structure, Fisher Information Matrix, a priori distributions |
| topic_facet | Diseño D-óptimo, Modelos no lineales, Estructura de correlación, Matriz de Información de Fisher, Distribuciones a priori D-optimal design, non-linear models, correlation structure, Fisher Information Matrix, a priori distributions |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/9504 |
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