Related papers: Estimating complete basis set extrapolation error …

This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…

Recent advances in uncertainty quantification increasingly emphasise the distinction between aleatory and epistemic uncertainty in machine learning, motivating the need for more unified frameworks. However, despite much progress in…

We study an optimization-based approach to construct statistically accurate confidence intervals for simulation performance measures under nonparametric input uncertainty. This approach computes confidence bounds from simulation runs driven…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the…

For the general parametric regression models with covariates contaminated with normal measurement errors, this paper proposes an accelerated version of the classical simulation extrapolation algorithm to estimate the unknown parameters in…

Among many efforts to facilitate timely access to safe and effective medicines to children, increased attention has been given to extrapolation. Loosely, it is the leveraging of conclusions or available data from adults or older age groups…

The method of extrapolating asymptotic series, based on the Self-Similar Approximation Theory, is developed. Several important questions are answered, which makes the foundation of the method unambiguous and its application straightforward.…

We present three different methods to estimate error bars on the predictions made using a neural network. All of them represent lower bounds for the extrapolation errors. For example, we did not include an analysis on robustness against…

We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty…

For the nonparametric regression models with covariates contaminated with normal measurement errors, this paper proposes an extrapolation algorithm to estimate the nonparametric regression functions. By applying the conditional expectation…

Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilistic uncertainty quantification and optimal experimental…

Inferring the causal effect of a non-randomly assigned exposure on an outcome requires adjusting for common causes of the exposure and outcome to avoid biased conclusions. Notwithstanding the efforts investigators routinely make to measure…

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…

We introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entire history. Our estimator is nothing more than a…

When implementing prediction models for high-stakes real-world applications such as medicine, finance, and autonomous systems, quantifying prediction uncertainty is critical for effective risk management. Traditional approaches to…

We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation…

In statistical inference, it is rarely realistic that the hypothesized statistical model is well-specified, and consequently it is important to understand the effects of misspecification on inferential procedures. When the hypothesized…

For a class of parametric modal regression models with measurement error, a simulation extrapolation estimation procedure is proposed in this paper for estimating the modal regression coefficients. Large sample properties of the proposed…

Classical approximation and learning methods are typically optimized for interpolation over a sampled domain {\Omega}, with no guarantees on their behavior in an extrapolation region {\Xi}, where small in-domain errors may amplify. We…