Related papers: Convergence Rates of Nonparametric Posterior Distr…

In this paper, we consider the well known problem of estimating a density function under qualitative assumptions. More precisely, we estimate monotone non increasing densities in a Bayesian setting and derive concentration rate for the…

In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In…

We analyze the posterior contraction rates of parameters in Bayesian models via the Langevin diffusion process, in particular by controlling moments of the stochastic process and taking limits. Analogous to the non-asymptotic analysis of…

In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…

We study the posterior contraction rates of a Bayesian method with Gaussian process priors in nonparametric regression and its plug-in property for differential operators. For a general class of kernels, we establish convergence rates of…

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…

Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…

We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…

Missing values are ubiquitous in (data) science, with potential detrimental consequences for any statistical analysis. As a consequence, a wealth of methods and theoretical results have been developed in recent years. Still, many questions…

Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…

In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the concept of posterior consistency and validate specific Bayesian methods, in terms of consistency of…

This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…

We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…

We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift…

We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…

In this work, we investigate the estimation of a parameter $f$ in PDEs using Bayesian procedures, and focus on posterior distributions constructed using Gaussian process priors, and its variational approximation. We establish contraction…