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Related Concept Videos

Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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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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Propagation of Uncertainty from Random Error00:59

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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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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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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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Interpretation of Confidence Intervals01:19

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
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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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Meso-Scale Particle Image Velocimetry Studies of Neurovascular Flows In Vitro
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On the Interpolation of Data with Normally Distributed Uncertainty for Visualization.

S Schlegel1, N Korn, G Scheuermann

  • 1University of Leipzig. schlegel@informatik.uni-leipzig.de

IEEE Transactions on Visualization and Computer Graphics
|September 11, 2015
PubMed
Summary
This summary is machine-generated.

Visualizing uncertain data, often Gaussian distributed, requires careful interpolation. This study shows standard linear methods are suboptimal, recommending geostatistics and machine learning techniques for better uncertainty visualization.

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Area of Science:

  • Data visualization
  • Scientific computing
  • Statistical modeling

Background:

  • Uncertain data is prevalent across science and engineering.
  • Gaussian distributions are commonly used to model data uncertainty.
  • Interpolation is crucial for visualizing uncertain data on fixed positions.

Purpose of the Study:

  • Analyze the impact of linear interpolation on visualizing Gaussian distributed uncertain data.
  • Identify superior methods for uncertainty visualization.

Main Methods:

  • Evaluation of standard linear interpolation schemes.
  • Application of geostatistical methods.
  • Utilization of machine learning techniques.

Main Results:

  • Linear interpolation schemes can distort the visualization of Gaussian distributed uncertainty.
  • Geostatistical and machine learning methods demonstrate favorable properties for uncertainty visualization.

Conclusions:

  • Standard interpolation methods are not ideal for visualizing Gaussian uncertain data.
  • Advanced techniques from geostatistics and machine learning offer improved solutions for uncertainty visualization.