A Note on Posterior Consistency of Nonparametric Poisson Regression Models

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 errors of types I and II.