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Simultaneous prediction for independent Poisson processes with different durations

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  • Komaki, Fumiyasu

Abstract

Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by the same parameter. The performance of predictive densities is evaluated by the Kullback–Leibler divergence. A class of prior distributions depending on the objective of prediction is introduced. A Bayesian predictive density based on a prior in this class dominates the Bayesian predictive density based on the Jeffreys prior.

Suggested Citation

  • Komaki, Fumiyasu, 2015. "Simultaneous prediction for independent Poisson processes with different durations," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 35-48.
    • Handle: RePEc:eee:jmvana:v:141:y:2015:i:c:p:35-48
    DOI: 10.1016/j.jmva.2015.06.008
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    References listed on IDEAS

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    1. Komaki, Fumiyasu, 2006. "A class of proper priors for Bayesian simultaneous prediction of independent Poisson observables," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1815-1828, September.
    2. Kobayashi, Kei & Komaki, Fumiyasu, 2008. "Bayesian shrinkage prediction for the regression problem," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1888-1905, October.
    3. George, Edward I. & Xu, Xinyi, 2008. "Predictive Density Estimation For Multiple Regression," Econometric Theory, Cambridge University Press, vol. 24(2), pages 528-544, April.
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    Citations

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    Cited by:

    1. Hamura, Yasuyuki & Kubokawa, Tatsuya, 2020. "Bayesian shrinkage estimation of negative multinomial parameter vectors," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    2. Yasuyuki Hamura & Tatsuya Kubokawa, 2022. "Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 515-536, May.
    3. Malay Ghosh & Tatsuya Kubokawa & Gauri Sankar Datta, 2020. "Density Prediction and the Stein Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 330-352, August.

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