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Related Concept Videos

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.
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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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Second Order systems I01:20

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Related Experiment Video

Updated: Jun 26, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Bayesian model order selection for nonlinear system function expansions.

Georgios D Mitsis1, Saad Jbabdi

  • 1Department of Electrical and Computer Engineering, National Technical University of Athens, Zografou 15780, Greece. gmitsis@esd.ntua.gr

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference
|January 24, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian approach for selecting parameters in Laguerre expansion models for systems identification. The method analytically derives model evidence and parameter distributions, improving model accuracy in physiological systems.

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Last Updated: Jun 26, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Systems Identification
  • Signal Processing
  • Computational Neuroscience

Background:

  • Orthonormal function expansions, particularly Laguerre basis expansions, are effective for reducing parameters in linear and nonlinear systems identification.
  • Laguerre expansions are well-suited for physiological systems due to their decaying characteristics and ability to model inherent nonlinearities.
  • Selecting structural parameters (model order, number of functions, Laguerre parameter alpha) is crucial but often relies on trial-and-error.

Purpose of the Study:

  • To formulate the Laguerre expansion technique within a Bayesian framework.
  • To analytically derive the posterior distribution of the Laguerre parameter alpha and model evidence.
  • To provide a statistically rigorous method for inferring expansion structural parameters.

Main Methods:

  • Bayesian inference applied to Laguerre expansion model identification.
  • Analytical derivation of the posterior distribution for the alpha parameter.
  • Calculation of model evidence for parameter selection.

Main Results:

  • The proposed Bayesian method enables analytical inference of the Laguerre parameter alpha and model evidence.
  • Demonstrated performance through simulated examples, validating the approach.
  • Comparison with alternative statistical criteria for model order selection.

Conclusions:

  • The Bayesian framework offers a robust alternative to trial-and-error for Laguerre expansion parameter selection.
  • The derived analytical results facilitate more accurate and efficient systems identification.
  • This approach enhances the application of Laguerre expansions in complex systems modeling.