The statistical aspects of determinantal point processes (DPPs) seem largely unexplored. We review the appealing properties of DDPs, demonstrate that they are useful models for repulsiveness, detail a simulation procedure, and provide freely available software for simulation and statistical inference. We pay special attention to stationary DPPs, where we give a simple condition ensuring their existence, construct parametric models, describe how they can be well approximated so that the likelihood can be evaluated and realizations can be simulated, and discuss how statistical inference is conducted using the likelihood or moment properties.

Keywords: maximum likelihood based inference, point process density, product densities, simulation, repulsiveness, spectral approach.