Related papers: On Bayesian based adaptive confidence sets for lin…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…

We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…

Piecewise constant priors are routinely used in the Bayesian Cox proportional hazards model for survival analysis. Despite its popularity, large sample properties of this Bayesian method are not yet well understood. This work provides a…

This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by…

It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is…

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection…

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…

Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…

This work deals with the ill-posed inverse problem of reconstructing a function $f$ given implicitly as the solution of $g = Af$, where $A$ is a compact linear operator with unknown singular values and known eigenfunctions. We observe the…

This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…

We construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by…

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…

This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…