• 제목/요약/키워드: Tibshirani's differential equation

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A BAYESIAN ANALYSIS FOR PRODUCT OF POWERS OF POISSON RATES

  • KIM HEA-JUNG
    • Journal of the Korean Statistical Society
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    • 제34권2호
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    • pp.85-98
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    • 2005
  • A Bayesian analysis for the product of different powers of k independent Poisson rates, written ${\theta}$, is developed. This is done by considering a prior for ${\theta}$ that satisfies the differential equation due to Tibshirani and induces a proper posterior distribution. The Gibbs sampling procedure utilizing the rejection method is suggested for the posterior inference of ${\theta}$. The procedure is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries. A salient feature of the procedure is that it provides a unified method for inferencing ${\theta}$ with any type of powers, and hence it solves all the existing problems (in inferencing ${\theta}$) simultaneously in a completely satisfactory way, at least within the Bayesian framework. In two examples, practical applications of the procedure is described.