Statistical aspects of determinantal point processes

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.