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Propagation of Uncertainty from Random Error00:59

Propagation 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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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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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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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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Estimating Population Mean with Known Standard Deviation01:16

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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Related Experiment Video

Updated: Dec 14, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Accounting for uncertainty in forest management models.

Francesca Rinaldi1, Ragnar Jonsson1

  • 1European Commission Joint Research Centre (JRC), Via E. Fermi, 2749 I-21027 Ispra, Italy.

Forest Ecology and Management
|July 21, 2020
PubMed
Summary

Forest owners can use robust optimization to manage forests effectively despite uncertainties like climate change. This approach leads to lower harvest levels, prioritizing long-term forest health over immediate revenue.

Keywords:
Climate changeControl theoryForest managementHarvesting decisionInformationUncertainty

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Area of Science:

  • Forestry Science
  • Environmental Economics
  • Control Theory

Background:

  • Forest production and ecosystem services face unpredictable changes due to climate change and market volatility.
  • Accurate impact assessment of these changes on forest management is challenging.

Purpose of the Study:

  • To introduce a robust optimization framework for forest management under uncertainty.
  • To investigate how model misspecification and information influence harvesting decisions.

Main Methods:

  • Utilized control theory to develop a robust optimization framework.
  • Employed a stylized forest model for simulations to explore uncertainty effects.
  • Analyzed the impact of information release on perceived uncertainty and behavior.

Main Results:

  • Model uncertainty significantly impacts harvesting intensity and forest development.
  • Forest managers concerned with uncertainty opt for lower harvest levels, prioritizing stand volume.
  • Information release alters perceived uncertainty, influencing harvesting behavior and forest outcomes.

Conclusions:

  • Robust optimization provides a viable strategy for forest management amidst uncertainty.
  • Addressing model uncertainty is crucial for sustainable forest development.
  • Information plays a key role in forest policy and management decisions.