Related papers: Reliable uncertainties in indirect measurements
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
I consider the task of experimental data fitting. Unlike the traditional approach I do not try to minimize any functional based on available experimental information, instead the minimization problem is replaced with constraint satisfaction…
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 the domain of physics experiments, data fitting is a pivotal technique for extracting insights from both experimental and simulated datasets. This article presents an approximation method designed to estimate the systematic errors…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…
This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
A common approach to synthetic data is to sample from a fitted model. We show that under general assumptions, this approach results in a sample with inefficient estimators and whose joint distribution is inconsistent with the true…
Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
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…
Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…
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…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…