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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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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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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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Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

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Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Precipitation gravimetry is based on converting an analyte into a sparingly soluble precipitate, which is separated by filtration and weighed. An ideal precipitate should be pure, insoluble, of known composition, and easily filtered from the reaction mixture.
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Watershed Planning within a Quantitative Scenario Analysis Framework
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A hierarchical Bayesian model averaging framework for groundwater prediction under uncertainty.

Nima Chitsazan1, Frank T-C Tsai

  • 1Department of Civil and Environmental Engineering, Louisiana State University, 3418G Patrick F. Taylor Hall, Baton Rouge, LA 70803.

Ground Water
|June 4, 2014
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Summary

This study introduces a hierarchical Bayesian model averaging (HBMA) method to address uncertainty in groundwater prediction models. HBMA effectively quantifies how different uncertainty sources impact chloride concentration predictions.

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Area of Science:

  • Environmental science
  • Hydrogeology
  • Computational modeling

Background:

  • Groundwater prediction models face significant uncertainty challenges.
  • Understanding and quantifying these uncertainties is crucial for reliable predictions.

Purpose of the Study:

  • To introduce a novel hierarchical Bayesian model averaging (HBMA) method.
  • To segregate, prioritize, and quantify sources of uncertainty in groundwater concentration prediction.

Main Methods:

  • Developed a BMA tree of models to analyze uncertainty propagation.
  • Applied HBMA to chloride concentration prediction in Baton Rouge, Louisiana.
  • Considered four sources of uncertainty, generating 180 flow and transport models.

Main Results:

  • Prediction variances from uncertain model elements significantly exceed those from uncertain parameters.
  • HBMA successfully quantifies the contribution of individual uncertainty sources to overall prediction uncertainty.

Conclusions:

  • The HBMA method provides a robust framework for uncertainty analysis in groundwater modeling.
  • Distinguishing between model element and parameter uncertainty is key for accurate predictions.