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Related Concept Videos

State Space Representation01:27

State Space Representation

734
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...
734
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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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.
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...
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State Space to Transfer Function01:21

State Space to Transfer Function

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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Transfer Function to State Space01:23

Transfer Function to State Space

964
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
964
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

408
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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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

1.1K
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
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Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
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Using model-based proposals for fast parameter inference on discrete state space, continuous-time Markov processes.

C M Pooley1, S C Bishop2, G Marion3

  • 1The Roslin Institute, The University of Edinburgh, Midlothian EH25 9RG, UK christopher.pooley@roslin.ed.ac.uk.

Journal of the Royal Society, Interface
|May 22, 2015
PubMed
Summary
This summary is machine-generated.

A new Bayesian statistics method, model-based proposal Markov chain Monte Carlo (MBP-MCMC), significantly speeds up inference for complex dynamic models. This approach is substantially faster than standard MCMC and particle MCMC, especially for multi-variable systems.

Keywords:
Bayesian inferenceMarkov chain Monte CarloMarkov processdiscrete state spaceepidemicparticle Markov chain Monte Carlo

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Area of Science:

  • Statistical modeling
  • Computational statistics
  • Dynamic systems analysis

Background:

  • Bayesian statistics integrates dynamic models with incomplete data for parameter inference.
  • Discrete state space, continuous-time Markov processes (DCTMPs) are key dynamic models used across scientific disciplines.
  • Efficient Bayesian inference for DCTMPs is crucial for analyzing complex systems.

Purpose of the Study:

  • To develop and evaluate a novel 'model-based proposal' (MBP) method for efficient Bayesian inference in DCTMPs.
  • To compare the performance of MBP-MCMC against standard MCMC and particle MCMC (PMCMC) techniques.
  • To assess the scalability and efficiency of MBP-MCMC with increasing model complexity and measurement dimensions.

Main Methods:

  • Development of a novel model-based proposal (MBP) algorithm for Markov chain Monte Carlo (MCMC) inference.
  • Application and comparison of MBP-MCMC, standard MCMC, and particle MCMC (PMCMC) using epidemiological models (SIS and SIR).
  • Evaluation of computational efficiency based on single-state variable and multi-state variable measurements.

Main Results:

  • MBP-MCMC demonstrated significant speed improvements over standard MCMC (at least 400-fold).
  • For single-state variable inference, MBP-MCMC was marginally faster (2-8 fold) than PMCMC.
  • For multi-state variable inference, MBP-MCMC vastly outperformed PMCMC (over 100-fold for four subpopulations), with efficiency gains increasing with complexity.

Conclusions:

  • MBP-MCMC offers a highly efficient computational framework for Bayesian inference in DCTMPs.
  • The method shows particular advantages in scenarios with complex models and multiple observed state variables.
  • MBP-MCMC represents a substantial advancement for analyzing dynamic systems in fields like epidemiology and ecology.