Abstract

TORRES, Llerzy  and  TOVAR CUEVAS, José Rafael. Method to Obtain a Vector of Hyperparameters: Application in Bernoulli Trials. Rev.Colomb.Estad. [online]. 2020, vol.43, n.2, pp.183-209.  Epub Dec 05, 2020. ISSN 0120-1751.  https://doi.org/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.

Keywords : Laplace's method; Bayesian inference; System of nonlinear equations.

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