Related papers: Supremum Norm Posterior Contraction and Credible S…

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…

We provide posterior contraction rates for constrained deep Gaussian processes in non-parametric density estimation and classication. The constraints are in the form of bounds on the values and on the derivatives of the Gaussian processes…

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…

This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve…

Sup-norm curve estimation is a fundamental statistical problem and, in principle, a premise for the construction of confidence bands for infinite-dimensional parameters. In a Bayesian framework, the issue of whether the…

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…

A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone…

The major goal of this paper is to study the second order frequentist properties of the marginal posterior distribution of the parametric component in semiparametric Bayesian models, in particular, a second order semiparametric…

We continue the investigation of Bernstein-von Mises theorems for nonparametric Bayes procedures from [Ann. Statist. 41 (2013) 1999-2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined,…

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…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

We consider the problem of shape restricted nonparametric regression on a closed set X ?\in R; where it is reasonable to assume the function has no more than H local extrema interior to X: Following a Bayesian approach we develop a…

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09,…

This article describes a robust algorithm to estimate a conditional probability density f(t|x) as a non-parametric smooth regression function. It is based on a neural network and the Bayesian interpretation of the network output as a…

In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…