Maximum-likelihood regression with systematic errors for astronomy and the physical sciences: II. Hypothesis testing of nested model components for Poisson data

A novel model of systematic errors for the regression of Poisson data is applied to hypothesis testing of nested model components with the introduction of a generalization of the $\Delta C$ statistic that applies in the presence of systematic errors. This paper shows that the null-hypothesis parent distribution of this $\Delta C_{sys}$ statistic can be obtained either through a simple numerical procedure, or in a closed form by making certain simplifying assumptions. It is found that the effects of systematic errors on the test statistic can be significant, and therefore the inclusion of sources of systematic errors is crucial for the assessment of the significance of nested model component in practical applications. The methods proposed in this paper provide a simple and accurate means of including systematic errors for hypothesis testing of nested model components in a variety of applications.