Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

Propagation of Uncertainty from Random Error

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...

Propagation of Uncertainty from Systematic Error

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...

BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

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.

State Space Representation

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...

Linear Approximation in Time Domain

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...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A close shave

Academic medicine : journal of the Association of American Medical Colleges·2000

Same author

Patchwork Sky

Academic medicine : journal of the Association of American Medical Colleges·2000

Same author

beta relaxation of nonpolymeric liquids close to the glass transition

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2000

Same author

Numerical investigation of the effects of classical phase space structure on a quantum system with decoherence

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2000

Same author

Momentum distributions for the quantum delta-kicked rotor with decoherence

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2000

Same author

Universal fluctuations in correlated systems

Physical review letters·2000

Search research articles

Related Experiment Video

Updated: Jul 12, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Bayesian reconstruction of chaotic dynamical systems

Meyer¹, Christensen

¹Department of Statistics, The University of Auckland, Auckland, New Zealand.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|November 23, 2000

Summary

This study introduces a Bayesian method using Markov chain Monte Carlo (MCMC) to accurately estimate parameters in nonlinear models from noisy time series data, correcting previous statistical flaws.

More Related Videos

Computational Reconstruction of Pancreatic Islets as a Tool for Structural and Functional Analysis

Computational Reconstruction of Pancreatic Islets as a Tool for Structural and Functional Analysis

Published on: March 9, 2022

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Related Experiment Videos

Last Updated: Jul 12, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Computational Reconstruction of Pancreatic Islets as a Tool for Structural and Functional Analysis

Computational Reconstruction of Pancreatic Islets as a Tool for Structural and Functional Analysis

Published on: March 9, 2022

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

Statistical Modeling
Computational Physics
Time Series Analysis

Background:

Determining parameters of nonlinear models from noisy time series data is a significant challenge.
Previous statistical approaches have exhibited flaws, leading to inaccurate parameter estimations.
Chaotic maps are complex nonlinear systems often encountered in scientific research.

Purpose of the Study:

To present a statistically sound Bayesian approach for parameter estimation in nonlinear models.
To address and correct the limitations of existing methods for time series analysis.
To apply a robust computational technique for analyzing chaotic systems.

Main Methods:

Utilized a Bayesian framework for parameter inference.
Employed a Markov chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler.
Detailed description of the Gibbs sampler methodology for parameter estimation.

Main Results:

Successfully estimated parameters of chaotic maps using the proposed Bayesian MCMC approach.
Demonstrated the statistical validity and accuracy of the Gibbs sampler for this problem.
Provided comprehensive statistical analysis supporting the method's efficacy.

Conclusions:

The Bayesian approach with Gibbs sampling offers a statistically rigorous solution for nonlinear model parameter estimation.
This method overcomes the limitations of prior statistically flawed techniques.
The presented approach is applicable to various real-world noisy time series data problems.