Related papers: Mixture representations and Bayesian nonparametric…
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…
This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an $L_1$ consistent estimator of $f$.…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
We consider the problem of boundary detection for areal data, focusing on situations where for each areal unit multiple observations are available. We propose a Bayesian nonparametric mixture model for the area-specific population…
The computation of two Bayesian predictive distributions which are discrete mixtures of incomplete beta functions is considered. The number of iterations can easily become large for these distributions and thus, the accuracy of the result…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
Structure and parameters in a Bayesian network uniquely specify the probability distribution of the modeled domain. The locality of both structure and probabilistic information are the great benefits of Bayesian networks and require the…
Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
In statistics, there are a variety of methods for performing model selection that all stem from slightly different paradigms of statistical inference. The reasons for choosing one particular method over another seem to be based entirely on…
The elicitation of an ordinal judgment on multiple alternatives is often required in many psychological and behavioral experiments to investigate preference/choice orientation of a specific population. The Plackett-Luce model is one of the…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…
This article is motivated by challenges in conducting Bayesian inferences on unknown discrete distributions, with a particular focus on count data. To avoid the computational disadvantages of traditional mixture models, we develop a novel…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
In population studies, it is standard to sample data via designs in which the population is divided into strata, with the different strata assigned different probabilities of inclusion. Although there have been some proposals for including…
We consider nonparametric inference for event time distributions based on current status data. We show that in this scenario conventional mixture priors, including the popular Dirichlet process mixture prior, lead to biologically…
Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…
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…