Bayesian Inference for Two-Parameter Gamma Distribution Assuming Different Noninformative Priors

• FERNANDO ANTONIO MOALA ^[1] ; PEDRO LUIZ RAMOS ^[1] ; JORGE ALBERTO ACHCAR ^[2]
  1. [1] Universidade Estadual Paulista

     Universidade Estadual Paulista

     Brasil

     
  2. [2] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 36, Nº. 2, 2013, págs. 319-336
• Idioma: inglés
• Títulos paralelos:
  • Inferencia Bayesiana para la distribución Gamma de dos parámetros asumiendo diferentes a prioris no informativas
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artículo diferentes distribuciones a priori son derivadas en una inferencia Bayesiana de la distribución Gamma de dos parámetros. A prioris no informativas tales como las de Jeffrey, de referencia, MDIP, Tibshirani y una priori innovativa basada en la alternativa por cópulas son investigadas. Se muestra que una a priori de información de datos maximales conlleva a una a posteriori impropia y que las diferentes escogencias del parámetro de interés permiten diferentes a prioris de referencia en este caso. Datos simulados permiten calcular las estimaciones Bayesianas e intervalos de credibilidad para los parámetros desconocidos así como la evaluación del desempeño de las distribuciones a priori evaluadas. El análisis Bayesiano se desarrolla usando métodos MCMC (Markov Chain Monte Carlo) para generar las muestras de la distribución a posteriori bajo las a priori consideradas.

  • English

    In this paper distinct prior distributions are derived in a Bayesian inference of the two-parameters Gamma distribution. Noniformative priors, such as Jeffreys, reference, MDIP, Tibshirani and an innovative prior based on the copula approach are investigated. We show that the maximal data information prior provides in an improper posterior density and that the different choices of the parameter of interest lead to different reference priors in this case. Based on the simulated data sets, the Bayesian estimates and credible intervals for the unknown parameters are computed and the performance of the prior distributions are evaluated. The Bayesian analysis is conducted using the Markov Chain Monte Carlo (MCMC) methods to generate samples from the posterior distributions under the above priors.

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