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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.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

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.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
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Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism
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Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

Jarad Niemi1, Mike West

  • 1Department of Statistical Science, Duke University, Durham, NC 27708-0251.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|June 22, 2010
PubMed
Summary

This study introduces a novel Markov chain Monte Carlo (MCMC) method for analyzing complex, non-linear models. The approach enhances inference for dynamic systems by accurately approximating hidden states and parameters.

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Published on: September 5, 2019

Area of Science:

  • Statistics
  • Computational Science
  • Systems Biology

Background:

  • State-space models are crucial for analyzing dynamic systems but pose challenges with non-linearities and non-Gaussian distributions.
  • Accurate inference of latent states and parameters is essential in fields like systems biology and finance.
  • Existing Markov chain Monte Carlo (MCMC) methods struggle with the complexity of non-linear, non-Gaussian state-space models.

Purpose of the Study:

  • To develop an efficient and accurate Markov chain Monte Carlo (MCMC) strategy for non-linear, non-Gaussian state-space models.
  • To enable robust inference on dynamic, latent state variables and fixed model parameters.
  • To provide a computational framework applicable to complex systems in science and engineering.

Main Methods:

  • A novel Metropolis-Hastings algorithm for state variables using sequential normal mixture approximations.
  • Accurate local mixture approximation to propagate densities through non-linearities.
  • A regenerating procedure to manage mixture component degeneracy.
  • Integration within a Gibbs sampler for incorporating uncertain fixed parameters.

Main Results:

  • Accurate approximations to sequential filtering and retrospective smoothing distributions.
  • Effective construction of global Metropolis proposal distributions for posterior simulation.
  • Successful application to a systems biology example and a stochastic volatility model.
  • Demonstrated capability for batch analysis of dynamic latent states.

Conclusions:

  • The proposed MCMC strategy offers a powerful tool for analyzing complex, non-linear, non-Gaussian state-space models.
  • The method provides accurate inference for both latent states and model parameters.
  • This approach has broad applicability in scientific and financial modeling requiring dynamic system analysis.