English
Related papers

Related papers: Statistical Guarantees for Data-driven Posterior T…

200 papers

We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for `many'…

Statistics Theory · Mathematics 2021-06-01 Ismaël Castillo , Stéphanie van der Pas

We study the coverage properties of full conformal regression in the proportional asymptotic regime where the ratio of the dimension and the sample size converges to a constant. In this setting, existing theory tells us only that full…

Statistics Theory · Mathematics 2025-03-03 Isaac Gibbs , Emmanuel J. Candès

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

Probability · Mathematics 2020-01-03 Marina Riabiz , Tohid Ardeshiri , Ioannis Kontoyiannis , Simon Godsill

Gaussian process models typically contain finite dimensional parameters in the covariance function that need to be estimated from the data. We study the Bayesian fixed-domain asymptotics for the covariance parameters in a universal kriging…

Statistics Theory · Mathematics 2022-09-27 Cheng Li

This work defines two classes of processes, that we term {\it tempered fractional multistable motion} and {\it tempered multifractional stable motion}. They are extensions of fractional multistable motion and multifractional stable motion,…

Probability · Mathematics 2019-07-04 Xiequan Fan , Jacques Lévy Véhel

Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…

Machine Learning · Computer Science 2026-03-12 Hanlin Yu , Marcelo Hartmann , Bernardo Williams , Mark Girolami , Arto Klami

We find the information geometry of tempered stable processes. Beginning with the derivation of $\alpha$-divergence between two tempered stable processes, we obtain the corresponding Fisher information matrices and the $\alpha$-connections…

Differential Geometry · Mathematics 2025-12-30 Jaehyung Choi

This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal…

Methodology · Statistics 2017-02-20 Xianyang Zhang , Anirban Bhattacharya

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…

Statistics Theory · Mathematics 2025-06-17 Mikołaj J. Kasprzak , Ryan Giordano , Tamara Broderick

A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…

Methodology · Statistics 2025-05-06 Martin Bladt , Jorge González Cázares

In this article densities (and their derivatives) of subordinators and inverse subordinators are considered. Under minor restrictions, generally milder than the existing in the literature, using a useful modification of the saddle point…

Probability · Mathematics 2024-02-12 Giacomo Ascione , Mladen Savov , Bruno Toaldo

We study posterior contraction rates for a class of deep Gaussian process priors applied to the nonparametric regression problem under a general composition assumption on the regression function. It is shown that the contraction rates can…

Statistics Theory · Mathematics 2022-08-16 Gianluca Finocchio , Johannes Schmidt-Hieber

We consider a general class of empirical-type likelihoods and develop higher order asymptotics with a view to characterizing members thereof that allow the existence of possibly data-dependent probability matching priors ensuring…

Statistics Theory · Mathematics 2008-12-18 Rahul Mukerjee

We present non-asymptotic two-sided bounds to the log-marginal likelihood in Bayesian inference. The classical Laplace approximation is recovered as the leading term. Our derivation permits model misspecification and allows the parameter…

Statistics Theory · Mathematics 2020-06-23 Anirban Bhattacharya , Debdeep Pati

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

Statistics Theory · Mathematics 2010-01-13 Yuan Liao , Wenxin Jiang

The paper discusses the reconstruction of potentials for quantum systems at finite temperatures from observational data. A nonparametric approach is developed, based on the framework of Bayesian statistics, to solve such inverse problems.…

Quantum Physics · Physics 2009-11-06 J. C. Lemm , J. Uhlig , A. Weiguny

When model uncertainty is handled by Bayesian model averaging (BMA) or Bayesian model selection (BMS), the posterior distribution possesses a desirable "oracle property" for parametric inference, if for large enough data it is nearly as…

Statistics Theory · Mathematics 2018-02-05 Wenxin Jiang , Cheng Li

Approximate Bayesian inference typically revolves around computing the posterior parameter distribution. In practice, however, the main object of interest is often a model's predictions rather than its parameters. In this work, we propose…

Machine Learning · Statistics 2026-05-29 Julian Rodemann , Alexander Marquard , Thomas Augustin , Michele Caprio

We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate…

Statistics Theory · Mathematics 2020-11-26 Kwangmin Lee , Kyoungjae Lee , Jaeyong Lee

Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…

Statistics Theory · Mathematics 2026-04-17 David T. Frazier , Christopher Drovandi , David J. Nott