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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.44 no.1 Bogotá Jan./June 2021 Epub Feb 27, 2021
https://doi.org/10.15446/rce.v44n1.83525
Original articles of research
Elicitation of the Parameters of Múltiple Linear Models
Elicitación de los parámetros de un modelo de regresión lineal múltiple
1Escuela de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Medellín, Colombia
2Grupo de Investigación Davinci, Facultad de Ciencias Exactas y Aplicadas, Instituto Tecnológico Metropolitano, Medellín, Colombia
Estimating the parameters of a multiple linear model is a common task in all areas of sciences. In order to obtain conjugate distributions, the Bayesian estimation of these parameters is usually carried out using noninformative priors. When informative priors are considered in the Bayesian estimation an important problem arises because techniques are required to extract information from experts and represent it in an informative prior distribution. Elicitation techniques can be used for such purpose even though they are more complex than the traditional methods.
In this paper, we propose a technique to construct an informative prior distribution from expert knowledge using hypothetical samples. Our proposal involves building a mental picture of the population of responses at several specific points of the explanatory variables of a given model and indirectly eliciting the mean and the variance at each of these points. In addition, this proposal consists of two steps: the first step describes the elicitation process and the second step shows a simulation process to estimate the model parameters.
Key words: Bayesian statistics; Conjugate distribution; Elicitation; Informative distribution
La estimación de los parámetros de un modelo de regresión lineal múltiple es una tarea común en todas las áreas de las ciencias. Con la idea de obtener distribuciones conjugadas, la estimación Bayesiana de estos parámetros se lleva a cabo usando distribuciones a priori no informativas. Un problema importante resulta cuando se incorporan distribuciones a priori informativas en la estimación Bayesiana, puesto que se hace necesario usar técnicas para extraer información de expertos, y representar dicha información en una distribución a prior informativa. Así, los métodos de elicitación pueden ser implementados para tal fin, a pesar de la complejidad de esta tarea en relación con las metodologías tradicionales.
En este paper, se propone un técnica para construir una distribución a priori informativa a partir de muestras hipotéticas usando información de expertos. Esta propuesta se basa en la construcción de un mapa mental de la población de respuestas en diferentes valores específicos de la variable explicativa en el modelo, y luego elicitar de forma indirecta la media y la varianza en cada uno de dichos valores de interés.
La propuesta es presentada en dos pasos, el primer paso describe el proceso de elicitación, y el segundo paso muestra un proceso de simulación para estimar los parámetros del modelo.
Palabras clave: Distribución conjugada; Distribución informativa; Elicitación; Estadística Bayesiana
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