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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: 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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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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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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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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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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Basics of Multivariate Analysis in Neuroimaging Data
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Multivariate Uncertainty in Deep Learning.

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    Accurately quantifying multivariate uncertainty in deep learning models is crucial for safe autonomous systems. This study models uncertainty for improved state estimation in robotics and autonomous vehicles.

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    Area of Science:

    • Robotics and Autonomous Systems
    • Machine Learning
    • State Estimation

    Background:

    • State estimation in autonomous systems relies on Kalman filters, often assuming fixed measurement uncertainties.
    • Deep learning models introduce variable, unpredictable uncertainties, posing risks to traditional methods.
    • Accurate multivariate uncertainty quantification is vital for safe and reliable deep learning integration.

    Purpose of the Study:

    • To develop a method for modeling multivariate uncertainty in neural networks for regression problems.
    • To incorporate both aleatoric and epistemic sources of heteroscedastic uncertainty.
    • To evaluate the impact of accurate uncertainty quantification on state estimation performance.

    Main Methods:

    • Developed a deep uncertainty covariance matrix model for neural networks.
    • Trained the model directly using a multivariate Gaussian density loss function.
    • Employed end-to-end training through a Kalman filter for indirect model optimization.

    Main Results:

    • Demonstrated significant performance improvements in a visual tracking task using accurate multivariate uncertainty.
    • Showcased the benefits for both in-domain and out-of-domain evaluation data.
    • Illustrated how end-to-end filter training enables uncertainty predictions to mitigate Kalman filter weaknesses in visual odometry.

    Conclusions:

    • Accurate multivariate uncertainty modeling is essential for robust deep learning in state estimation.
    • The proposed methods enhance the safety and reliability of autonomous vehicle and robotics applications.
    • End-to-end training offers a powerful approach to leverage uncertainty predictions for improved filter performance.