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Title: Bayesian nonparametric dynamic clustering: An application to gender stereotypes in words Authors:  Alessandra Guglielmi - Politecnico di Milano (Italy) [presenting]
Maria De Iorio - Yale-NUS College (Singapore)
Stefano Favaro - University of Torino and Collegio Carlo Alberto (Italy)
Lifeng Ye - UCL (United Kingdom)
Abstract: A probability model is proposed for a collection of random distributions indexed by time. The model is based on the dependent Dirichlet process prior and dependence among the random measures is introduced via latent variables, through a Gaussian copula transformation of a stationary autoregressive process of order one. This allows us to introduce time dependence among the random distributions. We propose a Sequential Monte Carlo algorithm to perform posterior inference in case of random densities given by mixtures of this time-dependent family of a.s. discrete distributions. We apply this model to a very interesting problem, to understand how gender stereotypes in words had changed over time in the 20th century. Other typical applications involve multiple time series in the biomedical context, as well as population density dynamics with areal data. Advantages of the proposed approach include wide applicability, ease of computations, interpretability and time dependent clustering of the observation. K-step nonparametric predictive density functions can be derived. The model retains desirable statistical properties for inference, while achieving substantial flexibility.