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Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
In recent years, there is a growing body of causal inference literature focusing on covariate balancing methods. These methods eliminate observed confounding by equalizing covariate moments between the treated and control groups. The…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
Quantile regression has been advocated in survival analysis to assess evolving covariate effects. However, challenges arise when the censoring time is not always observed and may be covariate-dependent, particularly in the presence of…
The Fisher Information Metric (FIM) and the associated Cram\'er-Rao Bound (CRB) are fundamental tools in statistical signal processing, which inform the efficient design of experiments and algorithms for estimating the underlying…
The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…
Randomized experiments are the "gold standard" for estimating causal effects, yet often in practice, chance imbalances exist in covariate distributions between treatment groups. If covariate data are available before units are exposed to…
Whereas confidence intervals are used to assess uncertainty due to unmeasured individuals, confounding intervals can be used to assess uncertainty due to unmeasured attributes. Previously, we have introduced a methodology for computing…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
ICME approaches provide decision support for materials design by establishing quantitative process-structure-property relations. Confidence in the decision support, however, must be achieved by establishing uncertainty bounds in ICME model…
Ratio-based biomarkers (RBBs), such as the proportion of necrotic tissue within a tumor, are widely used in clinical practice to support diagnosis, prognosis, and treatment planning. These biomarkers are typically estimated from…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…
Quantum coherence, a basic feature of quantum mechanics residing in superpositions of quantum states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical…
Propagating uncertainties introduced by chemical reaction rate parameters to high-fidelity numerical simulations of complex combustion devices is necessary to ascertain impact on computational predictions. However, the high cost of detailed…
Propensity score methods are an important tool to help reduce confounding in non-experimental studies. Most propensity score methods assume that covariates are measured without error. However, covariates are often measured with error, which…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. The conventional approach of model building…
With the increased accuracy and angular scale coverage of the recent CMB experiments it has become important to include calibration and beam uncertainties when estimating cosmological parameters. This requires an integration over possible…
This work presents a rigorous statistical and geometric framework for analyzing turbulence-impacted beam propagation and image topology with results obtained using a PMMA slab. The approach models beam intensity distributions as…