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Related Concept Videos

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
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Uncertainty: Overview00:59

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...

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Related Experiment Video

Updated: Jun 5, 2026

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat
11:18

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

Failure probability under parameter uncertainty.

R Gerrard1, A Tsanakas

  • 1Cass Business School, City University London, London, UK.

Risk Analysis : an Official Publication of the Society for Risk Analysis
|December 24, 2010
PubMed
Summary

Parameter uncertainty in risk analysis increases failure probability. This study provides exact failure probability calculations, independent of unknown parameters, for various loss distributions, enabling better risk control strategies.

Related Experiment Videos

Last Updated: Jun 5, 2026

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat
11:18

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

Area of Science:

  • Quantitative Risk Analysis
  • Financial Mathematics
  • Statistical Modeling

Background:

  • Risk analysis often involves a random factor exceeding a threshold, with failure probability controllable by setting this threshold.
  • Parameter uncertainty in risk factor distributions can undermine control measures, leading to unexpected failures.
  • Applications include environmental, supply chain, and insurance solvency risks.

Purpose of the Study:

  • To quantify the impact of parameter uncertainty on failure probabilities in risk analysis.
  • To develop methods for calculating exact failure probabilities despite unknown distribution parameters.
  • To explore and reconcile different approaches to controlling failure probabilities.

Main Methods:

  • Analysis of failure probabilities for loss distributions derived from increasing transformations of location-scale families (e.g., log-normal, Weibull, Pareto).
  • Derivation of exact failure probability calculations independent of unknown distribution parameters.
  • Comparison of frequentist/regulatory and Bayesian/personalistic approaches to risk control.

Main Results:

  • Parameter uncertainty demonstrably increases the expected frequency of failures.
  • Exact failure probabilities can be calculated for a broad class of distributions, offering an explicit measure of uncertainty's effect.
  • Two control strategies—reducing nominal failure probability and modifying the risk distribution model—are shown to be consistent.

Conclusions:

  • Explicit calculation of failure probabilities under parameter uncertainty is feasible and essential for effective risk management.
  • Both frequentist and Bayesian approaches can achieve desired failure probabilities, offering flexibility in risk control.
  • The study highlights the importance of considering data pooling and systemic risk implications.