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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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Related Experiment Video

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Spatial variability and uncertainty associated with soil moisture content using INLA-SPDE combined with PyMC3

Yujian Yang1, Xueqin Tong2

  • 1School of Civil Engineering and Geomatics, Shandong University of Technology, Zibo, 255000, Shandong Province, China. yyjtshkh@126.com.

Scientific Reports
|October 12, 2024
PubMed
Summary

This study develops a data-driven model to understand spatial variability and uncertainty in soil volumetric moisture content (SVMC) for winter wheat. Bayesian inference with INLA-SPDE provides robust predictions and quantifies uncertainty, improving moisture prediction accuracy.

Keywords:
Cauchy priorINLA-SPDE modelSoil moisture contentTransparency and interpretabilityUncertainty

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Area of Science:

  • Agricultural Science
  • Geospatial Analysis
  • Soil Science

Background:

  • Spatial variability in soil volumetric moisture content (SVMC) impacts prediction accuracy.
  • Accurate SVMC data is vital for agricultural management, especially during critical crop growth stages.

Purpose of the Study:

  • To develop a data-driven model for assessing spatial variability and uncertainty in SVMC.
  • To enhance the accuracy and interpretability of soil moisture predictions.

Main Methods:

  • Grid sampling of SVMC using Time Domain Reflectometry (TDR) in a 3-ha field.
  • Bayesian inference employing PyMC3 with Integrated Nested Laplace Approximation and Stochastic Partial Differential Equation (INLA-SPDE) model.
  • Utilizing Markov-Chain Monte-Carlo (MCMC) trace plots, Kernel Density Estimates (KDE), and rank plots for model transparency.

Main Results:

  • The developed model accurately predicted SVMC and quantified uncertainty using 95% credible intervals.
  • A Cauchy prior demonstrated greater robustness than a Gaussian prior for SVMC prediction.
  • Model transparency and interpretability were achieved through various visualization techniques.

Conclusions:

  • Bayesian inference with INLA-SPDE effectively addresses spatial heterogeneity and uncertainty in SVMC.
  • The model provides a robust and interpretable framework for soil moisture prediction.
  • Explicit quantification of SVMC uncertainty is achievable through highest-posterior density intervals.