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Related Concept Videos

Uncertainty: Overview00:59

Uncertainty: Overview

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.
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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 't,' or...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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...
Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

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Related Experiment Videos

Declarative representation of uncertainty in mathematical models.

Andrew K Miller1, Randall D Britten, Poul M F Nielsen

  • 1Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand. ak.miller@auckland.ac.nz

Plos One
|July 18, 2012
PubMed
Summary

This study introduces a method to declaratively describe parameter uncertainty in CellML models, enabling robust simulations. The approach extends CellML and Simulation Experiment Description Markup Language (SED-ML) for uncertainty analysis.

Related Experiment Videos

Area of Science:

  • Computational Biology
  • Mathematical Modeling
  • Systems Biology

Background:

  • Standardized exchange formats like CellML and SBML facilitate mathematical model sharing.
  • Existing standards lack mechanisms for describing parameter uncertainty, a crucial aspect of real-world systems.
  • Parameter uncertainty arises from measurement errors, unknown values, or population variability.

Purpose of the Study:

  • To present a declarative approach for describing parameter uncertainty in CellML models.
  • To extend the Simulation Experiment Description Markup Language (SED-ML) for sampling sensitivity analysis.
  • To demonstrate the usability of the proposed uncertainty specification through implementation and simulation.

Main Methods:

  • Utilized CellML extension mechanisms to declaratively encode parameter uncertainty.
  • Described uncertainty using univariate continuous probability density functions or multiple realisations.
  • Developed a software implementation within the CellML API for uncertainty specification and SED-ML extension.
  • Performed sampling sensitivity analyses on encoded models.

Main Results:

  • Successfully encoded parameter uncertainty in CellML models.
  • Implemented a software library supporting the uncertainty specification and SED-ML extension.
  • Demonstrated the capability to run meaningful simulations on models with encoded uncertainty.
  • Validated the approach through sampling sensitivity analyses.

Conclusions:

  • The proposed declarative approach effectively represents parameter uncertainty in CellML.
  • The developed software implementation enables robust uncertainty quantification and sensitivity analysis.
  • This work enhances the utility of CellML for modeling systems with inherent parameter variability.