Related papers: Bayesian multivariate mixed-scale density estimati…

Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of…

In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood…

In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of…

The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

Analysis of observational studies increasingly confronts the challenge of determining which of a possibly high-dimensional set of available covariates are required to satisfy the assumption of ignorable treatment assignment for estimation…

Clustering multivariate binary data is of interest in many scientific fields, including ecology, biomedicine, and social policy. Beyond heuristic clustering algorithms, such data can be modelled using multivariate Bernoulli mixture models.…

We develop a nonparametric Bayesian modeling framework for clustered ordinal responses in developmental toxicity studies, which typically exhibit extensive heterogeneity. The primary focus of these studies is to examine the dose-response…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…

Conditional density estimation generalizes regression by modeling a full density f(yjx) rather than only the expected value E(yjx). This is important for many tasks, including handling multi-modality and generating prediction intervals.…

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…

We study Bayes procedures for the problem of nonparametric drift estimation for one-dimensional, ergodic diffusion models from discrete-time, low-frequency data. We give conditions for posterior consistency and verify these conditions for…

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…

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where…

We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution $P_0$, which may not be in the support of the prior, we show that the posterior…

Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are…