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In this paper we consider the problem of dynamic clustering, where clustermemberships may change over time and clusters may split and merge over time,thus creating new clusters and destroying existing ones. We propose a Bayesiannonparametric approach to dynamic clustering via mixture modeling. Our approachrelies on a novel time-dependent nonparametric prior defined by combining: i) acopula-based transformation of a Gaussian autoregressive process; ii) thestick-breaking construction of the Dirichlet process. Posterior inference isperformed through a particle Markov chain Monte Carlo algorithm which issimple, computationally efficient and scalable to massive datasets. Advantagesof the proposed approach include flexibility in applications, ease ofcomputations and interpretability. We present an application of our dynamicBayesian nonparametric mixture model to the study the temporal dynamics ofgender stereotypes in adjectives and occupations in the 20th and 21st centuriesin the United States. Moreover, to highlight the flexibility of our model wepresent additional applications to time-dependent data with covariates and withspatial structure.

Bayesian nonparametric temporal dynamic clustering via autoregressive Dirichlet priors