Related papers: The Dirichlet Process with Large Concentration Par…
The large deviation principle is established for the Poisson--Dirichlet distribution when the parameter $\theta$ approaches infinity. The result is then used to study the asymptotic behavior of the homozygosity and the Poisson--Dirichlet…
We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and…
In analytic number theory, the Selberg--Delange Method provides an asymptotic formula for the partial sums of a complex function $f$ whose Dirichlet series has the form of a product of a well-behaved analytic function and a complex power of…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…
Dirichlet distributions are probability measures on the unit simplex. They are often used as prior distributions in modeling categorical data, such as in topic analysis of text data. Motivated by this application, we consider Monte Carlo…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
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…
Consider ``stochastic differential equations" driven by fractional Brownian motion with Hurst parameter H (1/4 <H< 1). Their solutions are sometimes called fractional diffusion processes. The main purpose of this paper is conditioning these…
In this paper we provide general conditions to check on the model and the prior to derive posterior concentration rates for data-dependent priors (or empirical Bayes approaches). We aim at providing conditions that are close to the…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
The recently developed semi-parametric generalized linear model (SPGLM) offers more flexibility as compared to the classical GLM by including the baseline or reference distribution of the response as an additional parameter in the model.…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. However, due to the flexibility of these models,…
We develop nonparametric Bayesian modelling approaches for Poisson processes, using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, such as the unit square,…
This paper develops some general calculus for GGC and Dirichlet process means functionals. It then proceeds via an investigation of positive Linnik random variables, and more generally random variables derived from compositions of a stable…
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…
In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a…