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Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…

Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…

We propose a Bayesian nonparametric model for mixed-type bounded data, where some variables are compositional and others are interval-bounded. Compositional variables are non-negative and sum to a given constant, such as the proportion of…

The conventional use of the Generalized Extreme Value (GEV) distribution to model block maxima may be inappropriate when extremes are actually structured into multiple heterogeneous groups. In this work, we propose a novel approach for…

Financial studies require volatility based models which provides useful insights on risks related to investments. Stochastic volatility models are one of the most popular approaches to model volatility in such studies. The asset returns…

Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input.…

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…

Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. Prior specification is, however, relatively…

In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data…

The compound Poisson process and the Dirichlet process are the pillar structures of Renewal theory and Bayesian nonparametric theory, respectively. Both processes have many useful extensions to fulfill the practitioners needs to model the…

Mixture models are well-known for their versatility, and the Bayesian paradigm is a suitable platform for mixture analysis, particularly when the number of components is unknown. Bhattacharya (2008) introduced a mixture model based on the…

Recently, the Bayesian nonparametric approach in survival studies attracts much more attentions. Because of multi modality in survival data, the mixture models are very common in this field. One of the famous priors on Bayesian…

When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…

This article establishes general conditions for posterior consistency of Bayesian finite mixture models with a prior on the number of components. That is, we provide sufficient conditions under which the posterior concentrates on…

The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…

Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even…

Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a…

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…

Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on…