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The use of high-dimensional data for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed…
In this project we are interested in performing clustering of observations such that the cluster membership is influenced by a set of predictors. To that end, we employ the Bayesian nonparameteric Common Atoms Model, which is a nested…
A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…
Models for dependent data are distinguished by their targets of inference. Marginal models are useful when interest lies in quantifying associations averaged across a population of clusters. When the functional form of a covariate-outcome…
We consider the problem of clustering nested or hierarchical data, where observations are grouped and there are both group-level and observation-level variables. In our motivating OneK1K dataset, observations consist of single-cell…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
The study of almost surely discrete random probability measures is an active line of research in Bayesian nonparametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant…
Although exchangeable processes from Bayesian nonparametrics have been used as a generating mechanism for random partition models, we deviate from this paradigm to explicitly incorporate clustering information in the formulation of our…
We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best…
We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to…
In this paper we propose a Bayesian nonparametric model for clustering partial ranking data. We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice…
An "element-free" probability distribution is what remains of a probability distribution after we forget the elements to which the probabilities were assigned. These objects naturally arise in Bayesian statistics, in situations where…
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…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
Model-based clustering is a powerful tool that is often used to discover hidden structure in data by grouping observational units that exhibit similar response values. Recently, clustering methods have been developed that permit…
The use of hierarchical mixture priors with shared atoms has recently flourished in the Bayesian literature for partially exchangeable data. Leveraging on nested levels of mixtures, these models allow the estimation of a two-layered data…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…
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…
Recent advances in topic models have explored complicated structured distributions to represent topic correlation. For example, the pachinko allocation model (PAM) captures arbitrary, nested, and possibly sparse correlations between topics…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…