  We consider mixture models where location parameters are a priori encouraged
to be well separated. We explore a class of determinantal point process (DPP)
mixture models, which provide the desired notion of separation or repulsion.
Instead of using the rather restrictive case where analytical results are
available, we adopt a spectral representation from which approximations to the
DPP intensity functions can be readily computed. For the sake of concreteness
the presentation focuses on a power exponential spectral density, but the
proposed approach is in fact quite general. We later extend our model to
incorporate covariate information in the likelihood and also in the assignment
to mixture components, yielding a trade-off between repulsiveness of locations
in the mixtures and attraction among subjects with similar covariates. We
develop full Bayesian inference, and explore model properties and posterior
behavior using several simulation scenarios and data illustrations.
