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Advances in Bayesian Modeling: Applications and Methods
Avances en modelamiento bayesiano: aplicaciones y métodos
DOI:
https://doi.org/10.15446/rce.v48n3.122850Keywords:
Bayesian inference, Markov chain Monte Carlo, Variational Approximation, Hierarchical modeling, Spatial modeling, Dirichlet process mixtures, Predictive analysis, Model evaluation. (en)Inferencia bayesiana, Cadenas de Markov de Monte Carlo, Aproximación variacional, Modelamiento jerárquico, Modelamiento espacial, Mezclas de procesos de Dirichlet, Análisis predictivo, Evaluación de modelos. (es)
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This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo techniques and variational approximations. Covering topics such as hierarchical modeling, spatial modeling, higher-order Markov chains, and Bayesian nonparametrics, the study emphasizes practical implementations across diverse fields, including oceanography, climatology, epidemiology, and astronomy. The aim is to bridge theoretical underpinnings with real-world applications, illustrating the formulation of Bayesian models, elicitation of priors, computational strategies, and posterior and predictive analyses. By leveraging different computational methods, this paper provides insights into model fitting, goodness-of-fit evaluation, and predictive accuracy, addressing computational efficiency and methodological challenges across various datasets and domains.
Este artículo explora la versatilidad y profundidad del modelado Bayesiano mediante la presentación de un amplio conjunto de aplicaciones y métodos, combinando técnicas de cadenas de Markov de Monte Carlo y aproximaciones variacionales. Al abarcar temas como modelamiento jerárquico, modelamiento espacial, cadenas de Markov de orden superior y métodos Bayesianos no paramétricos, el estudio enfatiza implementaciones prácticas en campos diversos, incluyendo oceanografía, climatología, epidemiología y astronomía. El objetivo es tender un puente entre los fundamentos teóricos y las aplicaciones del mundo real, ilustrando la formulación de modelos Bayesianos, la elicitación de distribuciones previas, las estrategias computacionales y los análisis posteriores y predictivos. Al aprovechar diferentes métodos computacionales, este trabajo ofrece una perspectiva sobre el ajuste de modelos, la evaluación de la bondad de ajuste y la precisión predictiva, abordando la eficiencia computacional y los desafíos metodológicos en distintos conjuntos de datos y dominios.
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