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04:08The Uncertainty Principle
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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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02:46Uncertainty in Measurement: Reading Instruments
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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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00:59Uncertainty: 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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03:34Uncertainty in Measurement: Significant Figures
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All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.
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00:54Uncertainty: 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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00:59Propagation of Uncertainty from Random Error
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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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Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations
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Optimal clustering under uncertainty.
Lori A Dalton1, Marco E Benalcázar2, Edward R Dougherty3
1Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, United States of America.
Plos One
|October 3, 2018
Summary
This study introduces an optimal robust clusterer using an effective random point process for improved predictive clustering. This framework minimizes misclustered points, enhancing accuracy in uncertain data scenarios.
Area of Science:
- * Computational statistics and machine learning.
- * Probabilistic modeling and data analysis.
Background:
- * Traditional clustering methods often lack predictive power or a robust error framework.
- * Existing probabilistic approaches, like the Bayes clusterer, require complete knowledge of the underlying point process.
Purpose of the Study:
- * To develop an optimal robust clusterer for situations with uncertainty in the point process.
- * To create a framework that minimizes misclustered points by incorporating randomness into the model.
Main Methods:
- * Derivation of an optimal robust clusterer through an effective random point process.
- * Incorporation of all randomness within the probabilistic structure of the point process.
- * Evaluation using synthetic mixtures of Gaussians and application to granular imaging.
Main Results:
- * An optimal robust clusterer was derived, analogous to robust classifiers.
- * The framework effectively handles uncertainty in the point process.
- * Demonstrated performance in synthetic data and practical application in granular imaging.
Conclusions:
- * The proposed method provides a robust clustering solution for uncertain data.
- * The framework successfully links robust clustering theory to granular imaging applications.
- * This approach enhances the predictive capabilities of clustering algorithms.