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Related Concept Videos

Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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...
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)...
Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
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...
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 Video

Updated: Jun 23, 2026

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
06:22

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

Published on: August 28, 2019

A stochastic model for the noise levels.

A Giménez1, M González

  • 1Ciencias Fisicas, Matematicas y de la Computacion, Universidad CEU-Cardenal Herrera, C/San Bartolome 55, Alfara del Patriarca (Valencia) 46115, Spain. algisan@uch.ceu.es

The Journal of the Acoustical Society of America
|May 12, 2009
PubMed
Summary

This study introduces a new stochastic model for predicting urban environmental noise levels, including L(den), L(day), L(evening), and L(night). The model uses Gaussian Ornstein-Uhlenbeck dynamics to capture noise variations and seasonal patterns.

Related Experiment Videos

Last Updated: Jun 23, 2026

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
06:22

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

Published on: August 28, 2019

Area of Science:

  • Environmental Science
  • Acoustics
  • Statistical Modeling

Background:

  • Urban noise pollution requires accurate prediction for effective mitigation.
  • Existing models may not fully capture the dynamic and seasonal nature of noise levels.

Purpose of the Study:

  • To introduce a novel stochastic model for predicting various urban noise metrics.
  • To analyze the mean-reversion properties and seasonal volatility of noise levels.

Main Methods:

  • Utilizing a Gaussian Ornstein-Uhlenbeck process to model noise level dynamics.
  • Separately analyzing noise dynamics for each day of the week to capture temporal variations.

Main Results:

  • The proposed stochastic model effectively describes and predicts L(den), L(day), L(evening), and L(night) levels.
  • Identified distinct mean-reversion properties and seasonal volatility patterns across different days of the week.

Conclusions:

  • The Gaussian Ornstein-Uhlenbeck model provides a robust framework for urban noise prediction.
  • Understanding daily and seasonal noise dynamics is crucial for developing targeted noise reduction strategies.