Related papers: Higher-order approximation for uncertainty quantif…
This paper considers the generation of prediction intervals (PIs) by neural networks for quantifying uncertainty in regression tasks. It is axiomatic that high-quality PIs should be as narrow as possible, whilst capturing a specified…
In this paper, we study the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is…
As data volume grows extensively, data profiling helps to extract metadata of large-scale data. However, one kind of metadata, order statistics, is difficult to be computed because they are not mergeable or incremental. Thus, the limitation…
We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…
Safety-critical navigation applications require that estimation errors be reliably quantified and bounded. This can be challenging for linear dynamic systems if the process noise or measurement errors have uncertain time correlation. In…
In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…
In nonclinical pharmaceutical development, tolerance intervals are critical in ensuring product and process quality. They are statistical intervals designed to contain a specified proportion of the population with a given confidence level.…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
Traditional statistical inference in cluster randomized trials typically invokes the asymptotic theory that requires the number of clusters to approach infinity. In this article, we propose an alternative conformal causal inference…
We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to…
We derive general bounds on the probability that the empirical first-passage time $\overline{\tau}_n\equiv \sum_{i=1}^n\tau_i/n$ of a reversible ergodic Markov process inferred from a sample of $n$ independent realizations deviates from the…
Interval estimation of quantiles has been treated by many in the literature. However, to the best of our knowledge there has been no consideration for interval estimation when the data are available in grouped format. Motivated by this, we…
We study confidence intervals based on hard-thresholding, soft-thresholding, and adaptive soft-thresholding in a linear regression model where the number of regressors $k$ may depend on and diverge with sample size $n$. In addition to the…
The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…
Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…
In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…