Related papers: Bayesian Nonparametric Estimation of a Unimodal De…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

Our focus is on constructing a multiscale nonparametric prior for densities. The Bayes density estimation literature is dominated by single scale methods, with the exception of Polya trees, which favor overly-spiky densities even when the…

In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples,…

The usefulness of Bayesian models for density and cluster estimation is well established across multiple literatures. However, there is still a known tension between the use of simpler, more interpretable models and more flexible, complex…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We…

In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based…

We propose algorithms for sampling from posterior path measures $P(C([0, T], \mathbb{R}^d))$ under a general prior process. This leverages ideas from (1) controlled equilibrium dynamics, which gradually transport between two path measures,…

Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on…

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector…

A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…

In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

Density functions that represent sample data are often multimodal, i.e. they exhibit more than one maximum. Typically this behavior is taken to indicate that the underlying data deserves a more detailed representation as a mixture of…

Finite mixtures are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to…

Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…

We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…

The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference…

The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general…

In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…