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Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…

Machine Learning · Computer Science 2025-12-05 Junyi Liu , Stanley Kok

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

Methodology · Statistics 2026-03-10 Adam Gorm Hoffmann , Claus Thorn Ekstrøm , Andreas Kryger Jensen

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…

Machine Learning · Computer Science 2021-06-15 Zhao-Zhou Li , Lu Li , Zhengyi Shao

Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…

Statistics Theory · Mathematics 2007-06-13 Wei Zhang

Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance…

Machine Learning · Statistics 2021-01-12 Sam Davanloo Tajbakhsh , Necdet Serhat Aybat , Enrique Del Castillo

This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…

Data Analysis, Statistics and Probability · Physics 2023-02-22 Krasymyr Tretiak , Georg Schollmeyer , Scott Ferson

Maximum approximate Bernstein likelihood estimates of the baseline density function and the regression coefficients in the proportional hazard regression models based on interval-censored event time data are proposed. This results in not…

Methodology · Statistics 2020-12-25 Zhong Guan

A two-stage approach is proposed to overcome the problem in quantile regression, where separately fitted curves for several quantiles may cross. The standard Bayesian quantile regression model is applied in the first stage, followed by a…

Methodology · Statistics 2015-02-05 Thais Rodrigues , Yanan Fan

Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…

Statistics Theory · Mathematics 2020-05-12 Toni Karvonen , George Wynne , Filip Tronarp , Chris J. Oates , Simo Särkkä

This paper reviews two main types of prediction interval methods under a parametric framework. First, we describe methods based on an (approximate) pivotal quantity. Examples include the plug-in, pivotal, and calibration methods. Then we…

Methodology · Statistics 2021-09-28 Qinglong Tian , Daniel J. Nordman , William Q. Meeker

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To…

Optimization and Control · Mathematics 2026-02-13 Ryan Cory-Wright , Andrés Gómez

In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes…

Numerical Analysis · Mathematics 2026-02-27 Tiantian Sun , Juan Zhang

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…

Computation · Statistics 2022-04-08 Willem van den Boom , Galen Reeves , David B. Dunson

This paper develops a new approach to post-selection inference for screening high-dimensional predictors of survival outcomes. Post-selection inference for right-censored outcome data has been investigated in the literature, but much…

Methodology · Statistics 2021-12-22 Tzu-Jung Huang , Alex Luedtke , Ian W. McKeague

Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…

Statistics Theory · Mathematics 2016-02-09 Samuel Balmand , Arnak Dalalyan

Prediction intervals in supervised Machine Learning bound the region where the true outputs of new samples may fall. They are necessary in the task of separating reliable predictions of a trained model from near random guesses, minimizing…

Machine Learning · Computer Science 2019-12-20 Anton Akusok , Yoan Miche , Kaj-Mikael Björk , Amaury Lendasse

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…

Computation · Statistics 2022-01-31 Jian Cao , Daniele Durante , Marc G. Genton

This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…

Statistics Theory · Mathematics 2025-06-05 Yuetian Luo , Chao Gao

This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…

Econometrics · Economics 2025-02-13 Jiti Gao , Fei Liu , Bin Peng , Yayi Yan

We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Joel Heinrich , Craig Blocker , John Conway , Luc Demortier , Louis Lyons , Giovanni Punzi , Pekka K. Sinervo