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Closed-Form Predictive Density Estimation for Bivariate Gamma Distribution With Application in Hydrological Flood Data
Estimación de densidad predictiva en forma cerrada para la distribución Gamma bivariada con aplicación en datos hidrológicos de inundaciones
DOI:
https://doi.org/10.15446/rce.v48n1.114461Keywords:
Bayes estimation, Bivariate gamma distribution, Hydrological event analysis, Kullback - Leibler divergence, Predictive density estimation. (en)Análisis de eventos hidrológicos, Divergencia de Kullback - Leibler, Distribución gamma bivariada, Estimación bayesiana, Estimación de densidad predictiva. (es)
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Finding closed-form solutions in Bayesian data analysis can be critical and time - saving, as it eliminates the need for computationally expensive techniques like MCMC methods. This paper explores Bayesian analysis with closed-form solutions of the bivariate gamma distribution. We present predictive density estimations under the Kullback - Leibler divergence, utilizing three well-known (non-) informative prior distributions, all analyzable in closed form. We compare these methods through simulation studies and a real-world example, applying them to hydrological flood data.
Encontrar soluciones en forma cerrada en el análisis de datos bayesiano puede ser fundamental y ahorrar tiempo, ya que elimina la necesidad de técnicas computacionalmente costosas como los métodos MCMC. Este artículo explora el análisis bayesiano con soluciones en forma cerrada para la distribución gamma bivariada. Presentamos estimaciones de densidad predictiva bajo la divergencia de Kullback-Leibler, utilizando tres distribuciones a priori bien conocidas (informativas y no informativas), todas analizables en forma cerrada. Comparamos estos métodos mediante estudios de simulación y un ejemplo del mundo real, aplicándolos a datos hidrológicos de inundaciones.
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