03: Goodness of fit Statistics for the Regression of Integer-count Data with Systematic Errors

Music City Center 

A new method that enables the use of systematic errors for the maximum-likelihood regression of integer-count Poisson data is presented. The method is based on the use of a phenomenological intrinsic model variance that describes the variability of the model, and it results in a goodness-of-fit statistic that is a simple modification of the usual Poisson deviance, which is also known in the astronomical community as the Cash statistic. A related statistic that is used for testing nested model components is also presented. The new methods presented in this talk aim to overcome the difficulty associated with the regression of integer-count data when there are sources of error that go beyond those of the data-generating process. The method is shown to be formally equivalent to the regression with data that are distributed according to a compounded and therefore overdispersed Poisson variable. Simple analytic forms for the null-hypothesis distributions of the statistics are also presented.

regression methods


Poisson distribution

systematic errors


goodness of fit statistics 

Astrostatistics Interest Group