Conjugate Analysis of the Conway-Maxwell-Poisson Distribution
By J. Kadane, Galit Shmueli, Tom Minka, Sharad Borle, Peter Boatwright. 2006
118 citations recorded by the source corpus.
This article explores a Bayesian analysis of a generalization of the Poisson distribution. By choice of a second parameter , both under-dispersed and over-dispersed data can be modeled. The Conway-Maxwell-Poisson distribu- tion forms an exponential family of distributions, so it has sucien t statistics of xed dimension as the sample size varies, and a conjugate family of prior distribu- tions. The article displays and proves a necessary and sucien t condition on the hyperparameters of the conjugate family for the prior to be proper, and it discusses methods of sampling from the conjugate distribution. An elicitation program to nd the hyperparameters from the predictive distribution is also discussed.
Subfields: Safety, Risk, Reliability and Quality, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ac25b3d58c1fec03d070dda64f982766017dca75
How researchers see this paper
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In Statistics and Probability
- Galit Shmueli
- Tom Minka
- A. Huang
- Kimberly F. Sellers
- Eric P. Xing
- Jeff Schneider
- Barnab'as P'oczos
- David M. Blei
Citations in the corpus
- A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution (2005, methodology): “A detailed analysis of the CMP conjugate family is given in Kadane et al. (2003) .”
- A Flexible Regression Model for Count Data (2010, unknown): “Although the Bayesian implementation allows for the incorporation of prior information in the form of prior parameter distributions [e.g., see Kadane et al. (2005)], the benefit of such information is useful only when informative priors are used and when the sample size is small.”