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Uncertainty: Overview00:59

Uncertainty: Overview

496
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.
496
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

3.1K
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...
3.1K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

621
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...
621
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

453
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...
453
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

884
Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
884
UV–Vis Spectrum01:30

UV–Vis Spectrum

1.0K
When light passes through a substance, a portion of the light is absorbed while the remaining light is reflected or transmitted. If the molecule absorbs light between the wavelengths of 180–400 nm range, the UV spectrum is obtained, and if it absorbs light in the 400–780 nm wavelength range, the visible spectrum is obtained.     
The UV–Vis spectrum of a molecule is the plot of its absorbance versus wavelength. The plot is drawn by taking molar...
1.0K

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Related Experiment Video

Updated: May 24, 2025

Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters
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Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters

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Uncertainty-Aware Spectral Visualization.

Marina Evers, Daniel Weiskopf

    IEEE Transactions on Visualization and Computer Graphics
    |March 4, 2025
    PubMed
    Summary
    This summary is machine-generated.

    This study visualizes data uncertainty in spectral analysis, including Fourier and wavelet spectra. The new method effectively represents non-normal uncertainty for better time series data exploration.

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    Area of Science:

    • Data analysis and visualization
    • Time series analysis
    • Spectral analysis

    Background:

    • Visualizing spectra like Fourier and wavelet spectra is crucial for identifying dominant frequencies in time series data.
    • Quantifying and visualizing data uncertainty in spectral analysis remains a challenge.

    Purpose of the Study:

    • To develop and visualize the propagation of data uncertainty to Fourier and continuous wavelet spectra.
    • To create an interactive approach for exploring uncertain time series data in both temporal and spectral domains.

    Main Methods:

    • Modeling time series as Gaussian processes to derive uncertainty propagation in spectra.
    • Utilizing percentile-based visualizations to encode non-normal uncertainty in 1D Fourier and 2D wavelet spectra.
    • Incorporating correlation, sensitivity, and signal-to-noise analysis into visualizations.

    Main Results:

    • The propagation of uncertainty results in weighted non-central chi-squared distributions within the spectrum.
    • Percentile-based visualizations effectively display non-normal uncertainty.
    • An interactive visualization tool was developed for exploring uncertain time series data.

    Conclusions:

    • The proposed method provides a robust way to visualize data uncertainty in spectral analysis.
    • The interactive approach enhances the investigation of time series data with uncertainty.
    • The approach was validated through real-world data sets and expert interviews.