A Note on Posterior Consistency of
Nonparametric Poisson Regression Models

Natesh S. Pillai, Robert L. Wolpert and Merlise A. Clyde

Duke University

July 2007

We introduce a new truncation approach to extend earlier methods for proving consistency in nonparametric Bayesian regression problems to non-compact state spaces. We illustrate the approach by proving posterior consistency for a nonparametric Poisson regression model. The key step is separating points in the parameter space by constructing hypothesis tests with suitably small error rates; we do this for individual pairs of points using our truncation approach, and then exploit the monotone likelihood-ratio property of the Poisson family to show that the tests have exponentially decaying probabilities of type I and II errors.

Keywords: Bayesian; nonparametric Poisson regression; posterior consistency; stochastic ordering; monotone likelihood ratio.

The manuscript is available PDF (136kb) format.

Cite as:

@TechReport{Pill:Wolp:Clyd:2007,
      Author = "Natesh S. Pillai and Robert L. Wolpert and Merlise A. Clyde",
       Title = "A Note on Posterior Consistency of Nonparametric {P}oisson
                Regression Models",
        Year = 2007,
 Institution = "Duke University Department of Statistical Science",
        Type = "Discussion Paper",
      Number = "2007-14",
         URL = "http://ftp.stat.duke.edu/WorkingPapers/07-14.html",
}