On Objective Priors for Testing Hypotheses About Some Poisson Models
In the absence of prior information, use of non-informative proper priors is often crucial for testing hypotheses, when using the Bayesian approach. In this context, the use of objective priors such as intrinsic priors and Zellner’s g-priors have gained much interest. In this paper, we consider the use of these priors for testing hypotheses about means and regression coefficients when observations come from Poisson distributions. We first derive an intrinsic prior for testing the equality of several Poisson means. We then focus on g-priors, giving a new motivation, based on shrinkage and minimal training sample arguments, for a mixture g-prior recommended by Liang, Paulo, Molina, Clyde and Berger (2008) for normal linear models. Using the same motivation, we propose a mixture g-prior for Poisson regression model. While the proposed g prior is similar to the one used by Wang and George (2007), it is also different in certain aspects. Specifically, we show that the Bayes factor derived from the proposed prior is consistent. We also provide examples using simulated and real data.
AMS Subject Classification62F15 62F03 62F05
KeywordsObjective Bayes Intrinsic priors g-priors Poisson means Poisson regression
Unable to display preview. Download preview PDF.
- Kass, R.E., Tierney, L., Kadane, J.B., 1990. The validity of posterior expansions based on Laplace’s method. In Essays in Honor of George Bernard, Geisser, S., Hodges, J.S., Press, S.J., Zellner, A. (editors), North Holland, Amsterdam, 473–488.Google Scholar
- Neter, J., Kutner, M.H., Wasserman, W., Nachtsheim, C.J., 1996. Applied Linear Statistical Models, McGraw-Hill, New York.Google Scholar
- Zellner, A., Siow, A., 1980. Posterior odds ratios for selected regression hypotheses. In Bayesian Statistics 1, Bernardo, J.M., DeGroot, M.H., Lindley, D.V., Smith, A.F.M. (editors), Valencia University Press, 585–603.Google Scholar