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We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

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…

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…

Dirichlet process (DP) mixture models provide a flexible Bayesian framework for density estimation. Unfortunately, their flexibility comes at a cost: inference in DP mixture models is computationally expensive, even when conjugate…

Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been…

Prior distributions play a crucial role in Bayesian approaches to clustering. Two commonly-used prior distributions are the Dirichlet and Pitman-Yor processes. In this paper, we investigate the predictive probabilities that underlie these…

A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures…

Nonparametric Bayesian approaches to clustering, information retrieval, language modeling and object recognition have recently shown great promise as a new paradigm for unsupervised data analysis. Most contributions have focused on the…

Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on…

Bayesian non-parametric methods based on Dirichlet process mixtures have seen tremendous success in various domains and are appealing in being able to borrow information by clustering samples that share identical parameters. However, such…

Finite mixture models, typically Gaussian mixtures, are well known and widely used as model-based clustering. In practical situations, there are many non-Gaussian data that are heavy-tailed and/or asymmetric. Normal inverse Gaussian (NIG)…

We consider the problem of estimating Shannon's entropy $H$ from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a…

There is an increasingly rich literature about Bayesian nonparametric models for clustering functional observations. However, most of the recent proposals rely on infinite-dimensional characterizations that might lead to overly complex…

We consider Bayesian nonparametric density estimation using a Pitman-Yor or a normalized inverse-Gaussian process kernel mixture as the prior distribution for a density. The procedure is studied from a frequentist perspective. Using the…

In recent years, there has been a growing demand to discern clusters of subjects in datasets characterized by a large set of features. Often, these clusters may be highly variable in size and present partial hierarchical structures. In this…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

In many real life problems, objects are described by large number of binary features. For instance, documents are characterized by presence or absence of certain keywords; cancer patients are characterized by presence or absence of certain…

Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…

Gibbs-type priors are widely used as key components in several Bayesian nonparametric models. By virtue of their flexibility and mathematical tractability, they turn out to be predominant priors in species sampling problems, clustering and…