Related papers: Methods to Compute Prediction Intervals: A Review …

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…

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…

A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…

For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…

This paper introduces new methods for constructing prediction intervals using quantile-based techniques. The procedures are developed for both classical (homoscedastic) autoregressive models and modern quantile autoregressive models. They…

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…

Prediction intervals are commonly used in meta-analysis with random-effects models. One widely used method, the Higgins-Thompson-Spiegelhalter prediction interval, replaces the heterogeneity parameter with its point estimate, but its…

This paper develops new insights into quantitative methods for the validation of computational model prediction. Four types of methods are investigated, namely classical and Bayesian hypothesis testing, a reliability-based method, and an…

This paper reviews the growing field of Bayesian prediction. Bayes point and interval prediction are defined and exemplified and situated in statistical prediction more generally. Then, four general approaches to Bayes prediction are…

We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems…

Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We…

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…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…

Accurate forecasting is one of the fundamental focus in the literature of econometric time-series. Often practitioners and policy makers want to predict outcomes of an entire time horizon in the future instead of just a single $k$-step…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

We construct long-term prediction intervals for time-aggregated future values of univariate economic time series. We propose computational adjustments of the existing methods to improve coverage probability under a small sample constraint.…

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…

We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…

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…