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We consider predictive inference using a class of temporally dependentDirichlet processes driven by Fleming--Viot diffusions, which have a naturalbearing in Bayesian nonparametrics and lend the resulting family of randomprobability measures to analytical posterior analysis. Formulating the impliedstatistical model as a hidden Markov model, we fully describe the predictivedistribution induced by these Fleming--Viot-driven dependent Dirichletprocesses, for a sequence of observations collected at a certain time givenanother set of draws collected at several previous times. This is identified asa mixture of P\'olya urns, whereby the observations can be values from thebaseline distribution or copies of previous draws collected at the same time asin the usual P\`olya urn, or can be sampled from a random subset of the datacollected at previous times. We characterise the time-dependent weights of themixture which select such subsets and discuss the asymptotic regimes. Wedescribe the induced partition by means of a Chinese restaurant processmetaphor with a conveyor belt, whereby new customers who do not sit at anoccupied table open a new table by picking a dish either from the baselinedistribution or from a time-varying offer available on the conveyor belt. Welay out explicit algorithms for exact and approximate posterior sampling ofboth observations and partitions, and illustrate our results on predictiveproblems with synthetic and real data.

Predictive inference with Fleming--Viot-driven dependent Dirichlet processes