Constructing Stationary Time Series of CRM’s via Bayesian Conjugacy

In this work, we develop a Bayesian nonparametric framework for modeling time-varying data in a generalized latent trait setting. While most Bayesian nonparametric methods are designed for static settings, many modern applications require priors that evolve over time. We address this need by introducing a unified class of time-dependent random measures for models with exponential-family likelihoods.

Our approach builds on conjugacy arguments from Bayesian parametric modeling and extends them to the nonparametric setting through a suitable class of completely random measures. This yields a tractable construction and induces flexible transition kernels for the latent random measures.
The resulting process admits a representation resembling a first-order autoregressive structure, providing both interpretability and a basis for richer temporal dependence structures. As a primary application, we focus on dynamic feature allocation models, in which the proposed framework naturally captures the emergence, disappearance, and reappearance of latent features over time.

Joint work with Alessandro Colombi (Bocconi University - Italy), Gim Griffin (University College London, UK)