Related papers: Les Probabilit\'es D\'efaillance comme Indicateurs…

The paper develops a novel and general methodology to characterize the nonlinearity of structural systems and to provide a mathematically proven basis for applying partial safety factors to nonlinear structural systems. It establishes, for…

While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety…

Previous studies have used a specific success metric within an algorithmic search framework to prove machine learning impossibility results. However, this specific success metric prevents us from applying these results on other forms of…

Experimentation platforms in industry must often deal with customer trust issues. Platforms must prove the validity of their claims as well as catch issues that arise. As a central quantity estimated by experimentation platforms, the…

Control systems operating in the real world face countless sources of unpredictable uncertainties. These random disturbances can render deterministic guarantees inapplicable and cause catastrophic safety failures. To overcome this, this…

We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…

This paper presents Bayesian techniques for conservative claims about software reliability, particularly when evidence suggests the software's executions are not statistically independent. We formalise informal notions of "doubting" that…

When assessing a software-based system, the results of Bayesian statistical inference on operational testing data can provide strong support for software reliability claims. For inference, this data (i.e. software successes and failures) is…

Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…

Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local…

In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…

Providing finite-time probabilistic safety and reach-avoid guarantees is crucial for safety-critical stochastic systems. Existing state-of-the-art barrier methods often rely on a restrictive boundedness assumption for auxiliary functions,…

Risk assessment instruments are used across the criminal justice system to estimate the probability of some future behavior given covariates. The estimated probabilities are then used in making decisions at the individual level. In the…

As the complexity of control systems increases, the need for systematic methods to guarantee their efficacy grows as well. However, direct testing of these systems is oftentimes costly, difficult, or impractical. As a result, the test and…

The use of tiered warnings and multicategorical forecasts are ubiquitous in meteorological operations. Here, a flexible family of scoring functions is presented for evaluating the performance of ordered multicategorical forecasts. Each…

The Brier score is frequently used by meteorologists to measure the skill of binary probabilistic forecasts. We show, however, that in simple idealised cases it gives counterintuitive results. We advocate the use of an alternative measure…

When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…

This paper presents a comprehensive review of univariate process capability indices (PCIs), which are critical metrics for assessing how effectively a manufacturing process satisfies customer specifications based on a single quality…

A new test for measuring the accuracy of financial market risk estimations is introduced. It is based on the probability integral transform (PIT) of the ex post realized returns using the ex ante probability distributions underlying the…

Regulation and risk management in banks depend on underlying risk measures. In general this is the only purpose that is seen for risk measures. In this paper we suggest that the reporting of risk measures can be used to determine the loss…