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Related Concept Videos

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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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...
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Uncertainty: Overview00:59

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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.
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Propagation of Uncertainty from Systematic Error01:10

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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...
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Uncertainty: Confidence Intervals00:54

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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...
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Numerical Calculations01:24

Numerical Calculations

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In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
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Significant Figures in Calculations00:58

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Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be determined by the following rules for rounding numbers:
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Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
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Probabilistic numerics and uncertainty in computations.

Philipp Hennig1, Michael A Osborne2, Mark Girolami3

  • 1Department of Empirical Inference , Max Planck Institute for Intelligent Systems , Tübingen, Germany.

Proceedings. Mathematical, Physical, and Engineering Sciences
|September 9, 2015
PubMed
Summary
This summary is machine-generated.

We advocate for probabilistic numerical methods, which quantify calculation uncertainties. These methods offer improved performance and a unified framework for managing errors in scientific computations.

Keywords:
inferencenumerical methodsprobabilitystatistics

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Area of Science:

  • Computational Science
  • Numerical Analysis
  • Scientific Computing

Background:

  • Numerical methods are essential in science and industry but suffer from precision loss.
  • Managing numerical uncertainty is critical for complex computations in fields like climate science and astrophysics.
  • Contemporary challenges necessitate robust methods for handling uncertainty in scientific data.

Purpose of the Study:

  • To promote the adoption of probabilistic numerical methods.
  • To demonstrate the benefits of interpreting classic numerical methods through a probabilistic lens.
  • To introduce new, adaptable probabilistic algorithms with improved empirical performance.

Main Methods:

  • Reinterpreting seminal numerical methods as probabilistic inference.
  • Developing new probabilistic algorithms adaptable to specific applications.
  • Applying probabilistic numerical methods to real-world problems in astrometry and astronomical imaging.

Main Results:

  • Probabilistic interpretation reveals new algorithmic possibilities.
  • New probabilistic algorithms show improved empirical performance.
  • Demonstrated benefits on astrometry and astronomical imaging problems.

Conclusions:

  • Probabilistic numerical methods provide a coherent framework for uncertainty quantification.
  • These methods enable better diagnosis and control of computational error sources.
  • Further research is needed to address open problems in probabilistic numerical algorithms.