Related papers: On a divergence-based prior analysis of stick-brea…
The Galton-Watson process is a model for population growth which assumes that individuals reproduce independently according to the same offspring distribution. Inference usually focuses on the offspring average as it allows to classify the…
Datasets containing large samples of time-to-event data arising from several small heterogeneous groups are commonly encountered in statistics. This presents problems as they cannot be pooled directly due to their heterogeneity or analyzed…
In nonclinical pharmaceutical development, tolerance intervals are critical in ensuring product and process quality. They are statistical intervals designed to contain a specified proportion of the population with a given confidence level.…
In [10], a `Markovian stick-breaking' process which generalizes the Dirichlet process $(\mu, \theta)$ with respect to a discrete base space ${\mathfrak X}$ was introduced. In particular, a sample from from the `Markovian stick-breaking'…
In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information…
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…
Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…
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…
For a long time, the Dirichlet process has been the gold standard discrete random measure in Bayesian nonparametrics. The Pitman--Yor process provides a simple and mathematically tractable generalization, allowing for a very flexible…
We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The alternative models are based on the principles of embedding…
One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive…
A new approach on the joint estimation of partially exchangeable observations is presented by constructing pairwise dependence between $m$ random density functions, each of which is modeled as a mixture of geometric stick breaking…
Consider a Dirichlet process mixture model (DPM) with random precision parameter $\alpha$, inducing $K_n$ clusters over $n$ observations through its latent random partition. Our goal is to specify the prior distribution…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
This paper introduces Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of $g$ priors that allow for differential shrinkage for various…
Modern regression analyses are often undermined by covariate measurement error, misspecification of the regression model, and misspecification of the measurement error distribution. We present, to the best of our knowledge, the first…