Related papers: Predictive inference with Fleming--Viot-driven dep…

We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent…

We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…

We introduce a nonparametric model for inferring time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and…

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…

We describe a procedure to introduce general dependence structures on a set of Dirichlet processes. Dependence can be in one direction to define a time series or in two directions to define spatial dependencies. More directions can also be…

Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…

We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose…

We study the distribution of the unobserved states of two measure-valued diffusions of Fleming-Viot and Dawson-Watanabe type, conditional on observations from the underlying populations collected at past, present and future times. If seen…

When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…

This paper provides a construction of a Fleming--Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of the Gibbs sampler based Markov processes. In particular, we concentrate on the…

One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive…

We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we…

For a long time, the Dirichlet process has been the gold standard discrete random measure in Bayesian nonparametrics. The Pitman--Yor process provides a simple and mathematically tractable generalization, allowing for a very flexible…

This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…

The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant…

We identify stationary distributions of generalized Fleming-Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures…

P\'olya urns are urns where at each unit of time a ball is drawn and replaced with some other balls according to its colour. We introduce a more general model: the replacement rule depends on the colour of the drawn ball and the value of…

Dirichlet process mixtures are particularly sensitive to the value of the precision parameter controlling the behavior of the latent partition. Randomization of the precision through a prior distribution is a common solution, which leads to…

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…