Related papers: Nonparametric Bayes inference on conditional indep…

In many real problems, dependence structures more general than exchangeability are required. For instance, in some settings partial exchangeability is a more reasonable assumption. For this reason, vectors of dependent Bayesian…

Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…

Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…

Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…

Parametric Bayesian modeling offers a powerful and flexible toolbox for machine learning. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we introduce a new class of…

In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying…

We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.

We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…

This paper is a note on the use of Bayesian nonparametric mixture models for continuous time series. We identify a key requirement for such models, and then establish that there is a single type of model which meets this requirement. As it…

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…

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…

The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with…

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…

Nonparametric and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity…

We set up a formal framework to characterize encompassing of nonparametric models through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for…

We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…

This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…