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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 particular...
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In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. However, sometimes, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000...
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Bayesian Approach for Inconsistent Information.

M Stein1, M Beer, V Kreinovich

  • 1Department of Civil and Environmental Engineering, National University of Singapore, Singapore.

Information Sciences
|October 4, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces fuzzy logic to the Bayesian approach, addressing inconsistencies between engineering data and prior knowledge caused by imprecise values. Fuzzy Bayesian methods offer a way to handle uncertainty, improving data processing in engineering applications.

Keywords:
Fuzzy-Bayesfuzzy random variablesimprecise dataimprecise probabilitiesuncertainty quantification

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Area of Science:

  • Engineering Data Analysis
  • Computational Statistics
  • Fuzzy Logic Systems

Background:

  • Traditional Bayesian methods assume exact data and prior knowledge.
  • Engineering data often contains imprecision due to measurement errors.
  • Inconsistencies arise when exact Bayesian assumptions conflict with real-world imprecise data.

Purpose of the Study:

  • To explore fuzzifying the Bayesian approach for engineering data processing.
  • To address inconsistencies between data and prior knowledge by incorporating imprecision.
  • To investigate the interaction between estimated imprecise parameters within a fuzzy Bayesian framework.

Main Methods:

  • Developing fuzzy versions of Bayesian formulas.
  • Implementing straightforward computations for fuzzy Bayesian expressions.
  • Analyzing the impact of imprecision on parameter estimation.

Main Results:

  • Fuzzy Bayesian approaches can reconcile data and prior knowledge despite imprecision.
  • Straightforward computations for fuzzy Bayesian formulas are currently time-consuming.
  • Identified the need for efficient reformulations of fuzzy Bayesian formulas for practical application.

Conclusions:

  • Fuzzy techniques offer a natural way to handle imprecision in Bayesian data processing.
  • Further research into algorithmic reformulations is needed to improve computational efficiency.
  • Optimized fuzzy Bayesian methods can enhance practical usability in engineering.