Method to Obtain a Vector of Hyperparameters: Application in Bernoulli Trials

• Published in: Revista Colombiana de estadística Vol. 43; no. 2; pp. 183 - 209
• Main Authors: Torres Ome, Llerzy Esneider, Tovar Cuevas, Jose Rafael
• Format: Journal Article
• Language: English
• Published: Bogota Universidad Nacional de Colombia 01.07.2020
• Subjects: Bayesian analysis; Bernoulli Hypothesis
• ISSN: 0120-1751; 2389-8976
• DOI: 10.15446/rce.v43n2.81744

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.