Related papers: Robust Prediction Interval estimation for Gaussian…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…
Gaussian process priors are a popular choice for Bayesian analysis of regression problems. However, the implementation of these models can be complex, and ensuring that the implementation is correct can be challenging. In this paper we…
A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…
Conformal Prediction methods have finite-sample distribution-free marginal coverage guarantees. However, they generally do not offer conditional coverage guarantees, which can be important for high-stakes decisions. In this paper, we…
We introduce a semi-parametric Bayesian model for survival analysis. The model is centred on a parametric baseline hazard, and uses a Gaussian process to model variations away from it nonparametrically, as well as dependence on covariates.…
Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations,…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
Gaussian process regression (GPR) is a powerful machine learning method which has recently enjoyed wider use, in particular in physical sciences. In its original formulation, GPR uses a square matrix of covariances among training data and…
In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of…
This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…
Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction…
Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
Over the last few decades, various methods have been proposed for estimating prediction intervals in regression settings, including Bayesian methods, ensemble methods, direct interval estimation methods and conformal prediction methods. An…
Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…