相关论文: Valid Credible Ellipsoids for Linear Functionals b…

In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…

Variational Bayes (VB) is a scalable alternative to Markov chain Monte Carlo (MCMC) for Bayesian posterior inference. Though popular, VB comes with few theoretical guarantees, most of which focus on well-specified models. However, models…

We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is…

Using normal approximation (NA) to construct a kernel-smoother-based confidence interval faces a fundamental challenge: the normalization makes a small estimation bias become a non-negligible inferential bias. This paper takes a different…

Bayesian hypothesis tests leverage posterior probabilities, Bayes factors, or credible intervals to inform data-driven decision making. We propose a framework for power curve approximation with such hypothesis tests. We present a fast…

The paper develops Bernstein von Mises Theorem under hierarchical $g$ -priors for linear regression models. The results are obtained both when the error variance is known, and also when it is unknown. An inverse gamma prior is attached to…

The order of smoothness chosen in nonparametric estimation problems is critical. This choice balances the tradeoff between model parsimony and data overfitting. The most common approach used in this context is cross-validation. However,…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

The classical B\"{u}hlmann credibility model has been widely applied to premium estimation for group insurance contracts and other insurance types. In this paper, we develop a robust B\"{u}hlmann credibility model using the winsorized…

The least squares (LS) estimate is the archetypical solution of linear regression problems. The asymptotic Gaussianity of the scaled LS error is often used to construct approximate confidence ellipsoids around the LS estimate, however, for…

Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…

This is a review of asymptotic and non-asymptotic behaviour of Bayesian methods under model specification. In particular we focus on consistency, i.e. convergence of the posterior distribution to the point mass at the best parametric…

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…

Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…

Valid uncertainty quantification after model selection remains challenging in high-dimensional linear regression, especially within the possibilistic inferential model (PIM) framework. We develop possibilistic inferential models for…

We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which…

Bayesian neural networks (BNNs) combine the expressive power of deep learning with the advantages of Bayesian formalism. In recent years, the analysis of wide, deep BNNs has provided theoretical insight into their priors and posteriors.…

Characterizing rectifiability of Radon measures in Euclidean space has led to fundamental contributions to geometric measure theory. Conditions involving existence of principal values of certain singular integrals…

We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…

A new computation method of frequentist $p$-values and Bayesian posterior probabilities based on the bootstrap probability is discussed for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is…