Including systematic uncertainties in confidence interval construction for Poisson statistics

One way to incorporate systematic uncertainties into the calculation of confidence intervals is by integrating over probability density functions parametrizing the uncertainties. In this paper we present a development of this method which takes into account uncertainties in the prediction of background processes and uncertainties in the signal detection efficiency and background efficiency, and allows for a correlation between the signal and background detection efficiencies. We implement this method with the likelihood ratio (usually denoted as the Feldman-Cousins) approach with and without conditioning. We present studies of coverage for the likelihood ratio and Neyman ordering schemes. In particular, we present two different types of coverage tests for the case where systematic uncertainties are included. To illustrate the method we show the relative effect of including systematic uncertainties in the case of the dark matter search as performed by modern neutrino telescopes.