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Related Concept Videos

Random Error01:04

Random Error

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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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Types of Errors: Detection and Minimization01:12

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Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or relative terms.
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
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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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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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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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Random and Systematic Errors01:20

Random and Systematic Errors

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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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Insights Into the Robustness of Minimum Error Entropy Estimation.

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    Minimum error entropy (MEE) offers robust regression, outperforming minimum mean square error (MMSE) with non-Gaussian noise. MEE provides accurate parameter estimates even with significant outliers in data.

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    Area of Science:

    • Information Theoretic Learning
    • Machine Learning
    • Statistical Inference

    Background:

    • Minimum Error Entropy (MEE) is a key optimization criterion in Information Theoretic Learning (ITL).
    • MEE minimizes prediction error entropy for regression, preserving data generating system information.
    • MEE estimators show superior performance and robustness against non-Gaussian noise compared to Minimum Mean Square Error (MMSE).

    Purpose of the Study:

    • To present theoretical results on the robustness of the MEE estimator.
    • To analyze MEE performance in the context of errors-in-variables (EIV) models.
    • To demonstrate MEE's resilience to outliers in regression problems.

    Main Methods:

    • Theoretical analysis of MEE robustness.
    • Derivation of a solution region for MEE in a one-parameter linear EIV model.
    • Verification of theoretical predictions through an illustrative example.

    Main Results:

    • MEE demonstrates strong robustness to various noise types, including non-Gaussian distributions.
    • A derived region containing the MEE solution indicates proximity to the true parameter value.
    • MEE estimates remain accurate despite arbitrarily large outliers in both input and output variables.

    Conclusions:

    • MEE is a highly robust optimization criterion for regression tasks, especially with noisy and outlier-prone data.
    • Theoretical findings support MEE's advantage over traditional methods like MMSE in challenging data conditions.
    • The study validates MEE's effectiveness through theoretical derivations and practical examples.