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As developers of libraries implementing interval arithmetic, we faced the same difficulties when it comes to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and…

Mathematical Software · Computer Science 2023-07-17 Luis Benet , Luca Ferranti , Nathalie Revol

As developers of libraries implementing interval arithmetic, we faced the same difficulties when it came to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and…

Numerical Analysis · Mathematics 2022-05-25 Nathalie Revol , Luis Benet , Luca Ferranti , Sergei Zhilin

Estimating the mode of a unimodal distribution is a classical problem in statistics. Although there are several approaches for point-estimation of mode in the literature, very little has been explored about the interval-estimation of mode.…

Statistics Theory · Mathematics 2025-04-01 Manit Paul , Arun Kumar Kuchibhotla

Control and state estimation procedures need to be robust against imprecisely known parameters, uncertainty in initial conditions, and external disturbances. Interval methods and other set-based techniques form the basis for the…

Systems and Control · Electrical Eng. & Systems 2025-10-22 Andreas Rauh , Marit Lahme , Simon Rohou , Luc Jaulin , Thach Ngoc Dinh , Tarek Raissi , Mohamed Fnadi

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…

Numerical Analysis · Mathematics 2021-07-14 Oliver Flatt , Pavel Panchekha

In the manufacturing industry, it is often necessary to repeat expensive operational testing of machine in order to identify the range of input conditions under which the machine operates properly. Since it is often difficult to accurately…

Machine Learning · Statistics 2019-10-29 Shogo Iwazaki , Yu Inatsu , Ichiro Takeuchi

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.…

Data Analysis, Statistics and Probability · Physics 2009-03-03 Marek W. Gutowski

Traditional hypothesis tests for differences between binomial proportions are at risk of being too liberal (Wald test) or overly conservative (Fisher's exact test). This problem is exacerbated in small samples. Regulators favour exact…

Methodology · Statistics 2025-07-31 Stef Baas , Yaron Racah , Elad Berkman , Sofia S. Villar

As with all measurements, the measurement of examinee ability, in terms of scores that the examinee obtains in a test, is also error-ridden. The quantification of such error or uncertainty in the test score data--or rather the complementary…

Applications · Statistics 2015-03-13 Satyendra Nath Chakrabartty , Kangrui Wang , Dalia Chakrabarty

A new method, with an application program in Matlab code, is proposed for testing item performance models on empirical databases. This method uses data intraclass correlation statistics as expected correlations to which one compares simple…

The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…

Information Theory · Computer Science 2016-05-18 Anusha Lalitha , Tara Javidi

This paper proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct…

Statistics Theory · Mathematics 2021-08-10 Igor Kheifets , Carlos Velasco

This paper considers the problem of designing interval observers for hidden mode switched nonlinear systems with bounded noise signals that are compromised by false data injection and switching attacks. The proposed observer consists of…

Systems and Control · Electrical Eng. & Systems 2021-11-04 Mohammad Khajenejad , Zeyuan Jin , Sze Zheng Yong

Objective: This paper proposes a framework to support the scientific research of standards so that they can be better measured, evaluated, and designed. Methods: Beginning with the notion of common models, the framework describes the…

Other Computer Science · Computer Science 2023-08-17 Enrico Coiera

We introduce a novel Interval Bound Propagation (IBP) approach for the formal verification of object detection models, specifically targeting the Intersection over Union (IoU) metric. The approach has been implemented in an open source…

Computer Vision and Pattern Recognition · Computer Science 2025-10-31 Noémie Cohen , Mélanie Ducoffe , Ryma Boumazouza , Christophe Gabreau , Claire Pagetti , Xavier Pucel , Audrey Galametz

In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…

Data Analysis, Statistics and Probability · Physics 2017-08-07 Marek W. Gutowski

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…

Methodology · Statistics 2020-06-18 Niccolò Dalmasso , Ann B. Lee , Rafael Izbicki , Taylor Pospisil , Ilmun Kim , Chieh-An Lin

Test generation and test data selection are difficult tasks for model based testing. Tests for a program can be meld to a test suite. A lot of research is done to quantify the quality and improve a test suite. Code coverage metrics estimate…

Software Engineering · Computer Science 2012-02-29 Dirk Richter , Christian Berg

This short study presents an opportunistic approach to a (more) reliable validation method for prediction uncertainty average calibration. Considering that variance-based calibration metrics (ZMS, NLL, RCE...) are quite sensitive to the…

Machine Learning · Statistics 2024-08-27 Pascal Pernot

In this paper in which we address the evaluation of measurement process quality, we mainly focus on the evaluation procedure, as far as it is based on the numerical measurement outcomes. We challenge the approach where the "exact" value of…

Methodology · Statistics 2013-02-05 Edgard Nyssen , Wolfgang Jacquet
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