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Related Concept Videos

Uncertainty: Overview00:59

Uncertainty: Overview

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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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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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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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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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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Related Experiment Video

Updated: Mar 24, 2026

An R-Based Landscape Validation of a Competing Risk Model
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An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

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Active Clustering with Model-Based Uncertainty Reduction.

Caiming Xiong, David M Johnson, Jason J Corso

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |March 16, 2016
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces an active semi-supervised spectral clustering method that intelligently selects human input to improve clustering accuracy. The novel framework maximizes human labor efficiency by reducing uncertainty during the clustering process.

    Related Experiment Videos

    Last Updated: Mar 24, 2026

    An R-Based Landscape Validation of a Competing Risk Model
    05:37

    An R-Based Landscape Validation of a Competing Risk Model

    Published on: September 16, 2022

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    Area of Science:

    • Machine Learning
    • Data Mining
    • Computer Vision

    Background:

    • Traditional clustering methods can be enhanced with human expertise (side information) for greater semantic meaning.
    • Current semi-supervised clustering methods often passively use pre-selected, potentially redundant, or detrimental human input.
    • Scaling semi-supervised algorithms requires active methods that strategically solicit human input for maximum impact.

    Purpose of the Study:

    • To propose a novel online framework for active semi-supervised spectral clustering.
    • To maximize the effectiveness of human labor by requesting input only where it has the greatest impact.
    • To reduce uncertainty during the clustering process by selecting pairwise constraints dynamically.

    Main Methods:

    • Developed an online framework for active semi-supervised spectral clustering.
    • Utilized uncertainty reduction as the core principle for selecting pairwise constraints.
    • Employed a first-order Taylor expansion to decompose uncertainty reduction into gradient and step-scale components.
    • Applied matrix perturbation theory and cluster-assignment entropy to compute these components.
    • Estimated the uncertainty reduction potential of each data sample.

    Main Results:

    • The proposed method effectively selects pairwise constraints as clustering progresses.
    • It consistently outperforms existing state-of-the-art techniques across diverse datasets (images, UCI, genes).
    • The method demonstrates robustness to noise and unknown numbers of clusters.
    • Validated through evaluations on image, UCI machine learning, and gene datasets.

    Conclusions:

    • The novel active semi-supervised spectral clustering framework significantly enhances clustering performance.
    • The uncertainty reduction principle and decomposition method are validated.
    • This approach offers a more efficient and effective way to leverage human expertise in clustering tasks.