  We discuss the use of the determinantal point process (DPP) as a prior for
latent structure in biomedical applications, where inference often centers on
the interpretation of latent features as biologically or clinically meaningful
structure. Typical examples include mixture models, when the terms of the
mixture are meant to represent clinically meaningful subpopulations (of
patients, genes, etc.). Another class of examples are feature allocation
models. We propose the DPP prior as a repulsive prior on latent mixture
components in the first example, and as prior on feature-specific parameters in
the second case. We argue that the DPP is in general an attractive prior model
for latent structure when biologically relevant interpretation of such
structure is desired. We illustrate the advantages of DPP prior in three case
studies, including inference in mixture models for magnetic resonance images
(MRI) and for protein expression, and a feature allocation model for gene
expression using data from The Cancer Genome Atlas. An important part of our
argument are efficient and straightforward posterior simulation methods. We
implement a variation of reversible jump Markov chain Monte Carlo simulation
for inference under the DPP prior, using a density with respect to the unit
rate Poisson process.
