Robust Bayesian nonparametric clustering across groups

Bayesian nonparametric mixtures for grouped data often identify clusters with shared mixture components. Small shifts between groups or departures from the component kernel can then fragment a population into several reported clusters. We introduce hierarchical shot-noise Cox process mixtures, which separate these two roles: group-specific local components estimate the densities, while shared latent centres, called rooms, link components into across-group clusters. Components in the same room may have distinct parameters. We derive prior moments, marginal and predictive laws, and a posterior representation supporting conditional Markov chain Monte Carlo inference. For univariate Gaussian mixtures, we establish density-posterior contraction under explicit regularity conditions, with rates comparable up to logarithmic factors to those available for hierarchical Dirichlet process mixtures. Under separate assumptions in a single-group, finite-activity setting, we prove uniform posterior tightness of the occupied-room count for data supported on a compact interval, without assuming a finite-mixture truth. This latter guarantee controls cluster proliferation without asserting recovery of a true partition. Simulations and a galaxy-data analysis illustrate how the construction accommodates variation across groups while retaining shared clusters.