Related papers: IID Sampling from Posterior Dirichlet Process Mixt…

We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose…

We consider the sequential sampling of species, where observed samples are classified into the species they belong to. We are particularly interested in studying some quantities describing the sampling process when there is a new species…

Motivation: With the development of droplet based systems, massive single cell transcriptome data has become available, which enables analysis of cellular and molecular processes at single cell resolution and is instrumental to…

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…

Sampling from binary quadratic distributions (BQDs) is a fundamental but challenging problem in discrete optimization and probabilistic inference. Previous work established theoretical guarantees for stochastic localization (SL) in…

We consider the Bayesian mixture of finite mixtures (MFMs) and Dirichlet process mixture (DPM) models for clustering. Recent asymptotic theory has established that DPMs overestimate the number of clusters for large samples and that…

While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittle's Likelihood, involving the second order…

Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…

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.…

While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing…

In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…

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…

We introduce a novel varying-weight dependent Dirichlet process (DDP) model that extends a recently developed semi-parametric generalized linear model (SPGLM) by adding a nonparametric Bayesian prior on the baseline distribution of the GLM.…

The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…

The Dirichlet Process (DP) mixture model has become a popular choice for model-based clustering, largely because it allows the number of clusters to be inferred. The sequential updating and greedy search (SUGS) algorithm (Wang and Dunson,…

Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

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…