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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.43 no.2 Bogotá July/Dec. 2020 Epub Dec 05, 2020
https://doi.org/10.15446/rce.v43n2.81744
Original articles of research
Method to Obtain a Vector of Hyperparameters: Application in Bernoulli Trials
Método para obtener un vector de hiperparámetros: aplicación en ensayos Bernoulli
1School of Statistics, Universidad del Valle, Cali, Colombia
The main difficulties when using the Bayesian approach are obtaining information from the specialist and obtaining hyperparameters values of the assumed probability distribution as representative of knowledge external to the data. In addition to the fact that a large part of the literature on this subject is characterized by considering prior conjugated distributions for the parameter of interest. An method is proposed to find the hyperparameters of a nonconjugated prior distribution. The following scenarios were considered for Bernoulli trials: four prior distributions (Beta, Kumaraswamy, Truncated Gamma and Truncated Weibull) and four scenarios for the generating process. Two necessary, but not sufficient conditions were identified to ensure the existence of a vector of values for the hyperparameter. The Truncated Weibull prior distribution performed the worst. The methodology was used to estimate the prevalence of two transmitted sexually infections in an Colombian indigenous community.
Key words: Laplace's method; Bayesian inference; System of nonlinear equations
Las principales dificultades cuando se utiliza el enfoque Bayesiano son la obtención de información del especialista y la obtención de valores de los hiperparámetros de la distribución de probabilidad asumida como representante del conocimiento a priori. Adicionalmente, gran parte de la literatura sobre este tema considera distribuciones a priori conjugadas para el parámetro de interés. Un método es propuesto para encontrar los valores de los hiperparámetros de una distribución a priori no conjugada. Los siguientes escenarios son considerados para ensayos Bernoulli: cuatro distribuciones a priori (Beta, Kumaraswamy, Gamma Truncada y Weibull Truncada) y cuatro escenarios para el proceso generador. Dos condiciones necesarias, pero no suficientes fueron identificadas para asegurar la existencia de un vector de valores para los hiperparámetros. La distribución a priori Weibull Truncada fue la que peor desempeño presentó. La metodología fue utilizada para estimar la prevalencia de dos infecciones de transmisión sexual en una comunidad indígena de Colombia.
Palabras clave: Método de Laplace; Inferencia bayesiana; Sistema de ecuaciones no lineales
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Received: June 2019; Accepted: May 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
