Related papers: An Alternative Prior Process for Nonparametric Bay…

We present an alternative approach to the Bayesian nonparametric analysis of conditional species richness under two-parameter Poisson Dirichlet priors. We rely on a known characterization by deletion of classes property and on results for…

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…

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…

In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…

Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…

In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of…

Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for…

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…

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and…

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…

Conjugate pairs of distributions over infinite dimensional spaces are prominent in statistical learning theory, particularly due to the widespread adoption of Bayesian nonparametric methodologies for a host of models and applications. Much…

Statistical modelling in the presence of data organized in groups is a crucial task in Bayesian statistics. The present paper conceives a mixture model based on a novel family of Bayesian priors designed for multilevel data and obtained by…

In this paper, we describe a Bayesian nonparametric approach to make inference for a bivariate spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all bivariate spherically symmetric…

Data sets for statistical analysis become extremely large even with some difficulty of being stored on one single machine. Even when the data can be stored in one machine, the computational cost would still be intimidating. We propose a…

Bayesian neural networks attempt to combine the strong predictive performance of neural networks with formal quantification of uncertainty associated with the predictive output in the Bayesian framework. However, it remains unclear how to…

This paper presents a novel clustering concept that is based on jointly learned nonlinear transforms (NTs) with priors on the information loss and the discrimination. We introduce a clustering principle that is based on evaluation of a…

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…

The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…

Robust tracking of a target in a clutter environment is an important and challenging task. In recent years, the nearest neighbor methods and probabilistic data association filters were proposed. However, the performance of these methods…