  We present a new class of cluster point process models, which we call
determinantal shot noise Cox processes (DSNCP), with repulsion between cluster
centres. They are the special case of generalized shot noise Cox processes
where the cluster centres are determinantal point processes. We establish
various moment results and describe how these can be used to easily estimate
unknown parameters in two particularly tractable cases, namely when the
offspring density is isotropic Gaussian and the kernel of the determinantal
point process of cluster centres is Gaussian or like in a scaled Ginibre point
process. Through a simulation study and the analysis of a real point pattern
data set we see that when modelling clustered point patterns, a much lower
intensity of cluster centres may be needed in DSNCP models as compared to shot
noise Cox processes.
