Related papers: Central limit theorems associated with the hierarc…
The hierarchical Pitman-Yor process is a discrete random measure used as a prior in Bayesian nonparametrics. It is motivated by the study of groups of clustered data exhibiting power law behavior. Our focus in this paper is on the Gaussian…
The Hierarchical Dirichlet process is a discrete random measure serving as an important prior in Bayesian non-parametrics. It is motivated with the study of groups of clustered data. Each group is modelled through a level two Dirichlet…
The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant…
This paper studies posterior concentration behavior of the base probability measure of a Dirichlet measure, given observations associated with the sampled Dirichlet processes, as the number of observations tends to infinity. The base…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
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…
Homogeneous normalized random measures with independent increments (hNRMIs) represent a broad class of Bayesian nonparametric priors and thus are widely used. In this paper, we obtain the strong law of large numbers, the central limit…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP…
We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general…
Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…
We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we…
This paper explores large sample properties of the two-parameter $(\alpha,\theta)$ Poisson--Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure, viewing this process as a natural extension…
Ferguson's Dirichlet process plays an important role in nonparametric Bayesian inference. Let $P_a$ be the Dirichlet process in $\mathbb{R}$ with a base probability measure $H$ and a concentration parameter $a>0.$ In this paper, we show…
We consider eigenvalues of generalized Wishart processes as well as particle systems, of which the empirical measures converge to deterministic measures as the dimension goes to infinity. In this paper, we obtain central limit theorems to…
Hypertensive disorders of pregnancy occur in about 10% of pregnant women around the world. Though there is evidence that hypertension impacts maternal cardiac functions, the relation between hypertension and cardiac dysfunctions is only…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…
Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…
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…