Bayesian Estimation for Linear Functions of Poisson Rates

Abstract

The probability matching prior for linear functions of Poisson parameters is derived. A comparison is made between the confidence intervals obtained by Stamey and Hamilton (2006), and the intervals derived by us when using the Jeffreys’ and probability matching priors. The intervals obtained from the Jeffreys’ prior are in some cases fiducial intervals (Krishnamoorthy and Lee, 2010). A weighted Monte Carlo method is used for the probability matching prior. The power and size of the test, using Bayesian methods, is compared to tests used by Krishnamoorthy and Thomson (2004). The Jeffreys’, probability matching and two other priors are used.

Keywords:

• Bayesian intervals
• Poisson parameters
• Power and size of test
• Probability matching prior, Weighted Monte Carlo method

Mathematics Subject Classification:

• 62C05
• 62C10
• 62F15

Acknowledgments

The authors would like to thank the referees and the editor for their valuable suggestions and comments which have improved this paper. The second author would like to thank the National Research Foundation of South Africa for their support.