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Volume 25 (2025)
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JP Journal of Biostatistics
JP Journal of Biostatistics
Volume 4, Issue 3, Pages 227 - 243 (October 2010)
SIMPLE EXACT BAYESIAN METHODS FOR INCORPORATING DIRECTIONAL PRIOR INFORMATION BASED ON A GENERALIZED
c
-DISTRIBUTION
Hisashi Noma
Abstract:
In many clinical and epidemiological studies, the prior knowledge or belief regarding treatment effect is clearly directional, i.e., pointing to protective effects or to harmful effects. Although recent developments in Bayesian computations such as the Markov Chain Monte Carlo methods have enabled to implement flexible modeling and inference, they involve complicated techniques and require additional special softwares. In this article, we develop exact Bayesian methods that can be conducted by simple concepts and computations. We consider a simple normal-approximated likelihood model and some class of skewed prior distributions. We introduce a generalized
c
-distribution, which constructs a conjugate family for the normal likelihood model, and show that it can be interpreted as a generalized model of the commonly-used normal prior model. We also show that the generalized
c
-distribution is derived as a posterior distribution by a gamma-prior model. In addition, we present simple exact computational methods for Bayesian inference based on the generalized
c
and gamma prior models. An application to an epidemiological study on the association of residential wire codes and magnetic fields with childhood leukemia is provided.
Keywords and phrases:
Bayesian methods, conjugate models, asymptotic normal approximation, a generalized
c
-distribution, gamma distribution.
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P-ISSN: 0973-5143
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