Related papers: Contaminated Gibbs-type priors
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
One of the main approaches used to construct prior distributions for objective Bayes methods is the concept of random imaginary observations. Under this setup, the expected-posterior prior (EPP) offers several advantages, among which it has…
Mixture regression models are powerful tools for capturing heterogeneous covariate-response relationships, yet classical finite mixtures and Bayesian nonparametric alternatives often suffer from instability or overestimation of clusters…
One of the most used priors in Bayesian clustering is the Dirichlet prior. It can be expressed as a Chinese Restaurant Process. This process allows nonparametric estimation of the number of clusters when partitioning datasets. Its key…
Gibbs random fields play an important role in statistics. However they are complicated to work with due to an intractability of the likelihood function and there has been much work devoted to finding computational algorithms to allow…
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…
Choosing the number of mixture components remains an elusive challenge. Model selection criteria can be either overly liberal or conservative and return poorly-separated components of limited practical use. We formalize non-local priors…
Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…
We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…
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…
We derive the class of normalized generalized Gamma processes from Poisson-Kingman models (Pitman, 2003) with tempered alfa-stable mixing distribution. Relying on this construction it can be shown that in Bayesian nonparametrics, results on…
Gibbs-type random probability measures, or Gibbs-type priors, are arguably the most "natural" generalization of the celebrated Dirichlet prior. Among them the two parameter Poisson-Dirichlet prior certainly stands out for the mathematical…
Feature allocation models are an extension of Bayesian nonparametric clustering models, where individuals can share multiple features. We study a broad class of models whose probability distribution has a product form, which includes the…
We explore the estimation of generalized additive models using basis expansion in conjunction with Bayesian model selection. Although Bayesian model selection is useful for regression splines, it has traditionally been applied mainly to…
Given an observed sample from a population of individuals belonging to species, "species-sampling" problems (SSPs) call for estimating some features of the unknown species composition of additional unobservable samples from the same…
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…
We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…
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…
Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…