Related papers: Hierarchical Species Sampling Models
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…
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…
This paper focuses on the problem of hierarchical non-overlapping clustering of a dataset. In such a clustering, each data item is associated with exactly one leaf node and each internal node is associated with all the data items stored in…
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…
Bayesian nonparametric hierarchical priors are highly effective in providing flexible models for latent data structures exhibiting sharing of information within and across groups. In this work, we focus on latent feature allocation models,…
We present the nested Chinese restaurant process (nCRP), a stochastic process which assigns probability distributions to infinitely-deep, infinitely-branching trees. We show how this stochastic process can be used as a prior distribution in…
The aim of the paper is to provide an exact approach for generating a Poisson process sampled from a hierarchical CRM, without having to instantiate the infinitely many atoms of the random measures. We use completely random measures~(CRM)…
We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…
A wide range of Bayesian models have been proposed for data that is divided hierarchically into groups. These models aim to cluster the data at different levels of grouping, by assigning a mixture component to each datapoint, and a mixture…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
Variable selection methods with nonlocal priors have been widely studied in linear regression models, and their theoretical and empirical performances have been reported. However, the crucial model selection properties for hierarchical…
This work focuses on clustering populations with a hierarchical dependency structure that can be described by a tree. A particular example that is the focus of our work is the phylogenetic tree, with nodes often representing biological…
This article introduces a novel framework for nonparametric priors on real-valued random vectors, which can be viewed as a multivariate generalization of neutral-to-the right priors. It is based on randomizing the exponent measure of a…
An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…
In this paper, we describe centering and noncentering methodology as complementary techniques for use in parametrization of broad classes of hierarchical models, with a view to the construction of effective MCMC algorithms for exploring…
Here we develop a method for performing nonparametric Bayesian inference on quantiles. Relying on geometric measure theory and employing a Hausdorff base measure, we are able to specify meaningful priors for the quantile while treating the…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
There has been increased interest in using prior information in statistical analyses. For example, in rare diseases, it can be difficult to establish treatment efficacy based solely on data from a prospective study due to low sample sizes.…
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…