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Related Concept Videos

Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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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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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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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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Uncertainty in Measurement: Accuracy and Precision03:37

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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. 
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Random Error01:04

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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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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Modeling Uncertainty for Gaussian Splatting.

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    Stochastic Gaussian Splatting (SGS) introduces uncertainty estimation for Gaussian Splatting (GS), improving novel-view synthesis. This framework enhances reliability and accuracy in generated images, aiding real-world applications.

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    Area of Science:

    • Computer Vision
    • Computer Graphics
    • Machine Learning

    Background:

    • Gaussian Splatting (GS) offers efficient, high-quality novel-view synthesis.
    • Current GS methods lack uncertainty quantification for synthesized views.
    • Neural Radiance Fields (NeRFs) provide confidence measures but are computationally expensive.

    Purpose of the Study:

    • To develop the first framework for uncertainty estimation in Gaussian Splatting (GS).
    • To integrate uncertainty prediction into the GS rendering pipeline.
    • To improve the reliability and accuracy of novel-view synthesis.

    Main Methods:

    • Introduced Stochastic Gaussian Splatting (SGS), a variational inference (VI)-based approach.
    • Integrated uncertainty prediction into the standard GS rendering pipeline.
    • Incorporated the area under sparsification error (AUSE) into the loss function for joint optimization.

    Main Results:

    • SGS demonstrated superior performance over existing methods on three datasets.
    • Achieved state-of-the-art results in both image rendering quality and uncertainty estimation accuracy.
    • Provided reliable insights into the confidence of synthesized views.

    Conclusions:

    • SGS effectively quantifies uncertainty in Gaussian Splatting.
    • The framework enhances the trustworthiness of novel-view synthesis.
    • Enables safer decision-making in real-world applications utilizing synthesized imagery.