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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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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
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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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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Estimating uncertainty in density surface models.

David L Miller1, Elizabeth A Becker2, Karin A Forney3,4

  • 1Centre for Research into Ecological & Environmental Modelling and School of Mathematics & Statistics, University of St Andrews, St Andrews, Fife, Scotland.

Peerj
|August 29, 2022
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Summary
This summary is machine-generated.

Estimating uncertainty in species distribution models is crucial for effective management. This study identifies uncertainty sources in density surface models and proposes a hybrid approach to quantify them, using fin whale data as an example.

Keywords:
Density surface modelsDistance samplingEnvironmental uncertaintyModel uncertaintySpatial modellingSpecies distribution modellingUncertainty quantification

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Area of Science:

  • Ecology
  • Marine Biology
  • Statistical Modeling

Background:

  • Species distribution models (SDMs) are vital for ecological management and conservation.
  • Quantifying uncertainty in SDM predictions is essential but often challenging.
  • Existing guidance on managing and combining uncertainty sources in SDMs is limited.

Purpose of the Study:

  • To identify and characterize sources of uncertainty in density surface models (DSMs).
  • To propose a flexible and modular approach for encapsulating these uncertainties.
  • To demonstrate the application of this approach using cetacean density modeling.

Main Methods:

  • Focus on density surface models, a spatial modeling technique for distance sampling data.
  • Development of an extensible, modular, hybrid analytical-simulation framework.
  • Application to fin whale (Balaenoptera physalus) density estimation in the California Current Ecosystem.

Main Results:

  • Detailed identification of where uncertainty can arise within the multi-stage DSM process.
  • Demonstration of a novel hybrid approach to systematically capture and combine uncertainty.
  • Empirical analysis of fin whale distribution and associated prediction uncertainty.

Conclusions:

  • The proposed hybrid approach offers a robust method for uncertainty quantification in DSMs.
  • This framework enhances the reliability of SDM predictions for marine mammal management.
  • Improved understanding of uncertainty aids conservation efforts for species like fin whales.