Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

956
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...
956
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

770
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...
770
Reducing Line Loss01:18

Reducing Line Loss

188
In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss...
188
Random Variables01:09

Random Variables

13.3K
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...
13.3K
Central Limit Theorem01:14

Central Limit Theorem

15.8K
The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
15.8K
Poisson Probability Distribution01:09

Poisson Probability Distribution

8.4K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
8.4K

You might also read

Related Articles

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

Sort by
Same author

The Capacity Gains of Gaussian Channels with Unstable Versus Stable Autoregressive Noise.

Entropy (Basel, Switzerland)·2025
Same author

New Formulas of Feedback Capacity for AGN Channels with Memory: A Time-Domain Sufficient Statistic Approach.

Entropy (Basel, Switzerland)·2025
Same author

Structural Properties of the Wyner-Ziv Rate Distortion Function: Applications for Multivariate Gaussian Sources.

Entropy (Basel, Switzerland)·2024
See all related articles

Related Experiment Video

Updated: Aug 28, 2025

Cross-Modal Multivariate Pattern Analysis
13:51

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

20.0K

A Realization Approach to Lossy Network Compression of a Tuple of Correlated Multivariate Gaussian RVs.

Charalambos D Charalambous1, Jan H van Schuppen2

  • 1Department of Electrical and Computer Engineering, University of Cyprus, P.O. Box 20537, CY-1678 Nicosia, Cyprus.

Entropy (Basel, Switzerland)
|September 23, 2022
PubMed
Summary

This study explores Gray and Wyner source coding for correlated Gaussian variables. It proves common information is achieved by a Gaussian variable, providing a formula based on canonical correlations.

Keywords:
Gray–Wyner networkWyner’s lossy common informationcanonical variable form of multivariate Gaussian random variablesmulti-user communicationweak realizations of conditional independence

More Related Videos

Author Spotlight: Emerging Technologies and Advanced Tools for Decoding Metabolomics Data Analysis
07:11

Author Spotlight: Emerging Technologies and Advanced Tools for Decoding Metabolomics Data Analysis

Published on: November 10, 2023

2.6K
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.0K

Related Experiment Videos

Last Updated: Aug 28, 2025

Cross-Modal Multivariate Pattern Analysis
13:51

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

20.0K
Author Spotlight: Emerging Technologies and Advanced Tools for Decoding Metabolomics Data Analysis
07:11

Author Spotlight: Emerging Technologies and Advanced Tools for Decoding Metabolomics Data Analysis

Published on: November 10, 2023

2.6K
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.0K

Area of Science:

  • Information Theory
  • Network Coding
  • Multivariate Statistics

Background:

  • The Gray and Wyner source coding problem addresses distributed compression of correlated data.
  • Understanding the fundamental limits of information transmission in networks is crucial.

Purpose of the Study:

  • To analyze Gray and Wyner source coding for correlated multivariate Gaussian random variables.
  • To characterize the rate region for a network with an encoder and two decoders.
  • To derive new results on Wyner's common information and its achievement.

Main Methods:

  • Utilizing weak stochastic realization and geometric approaches for random variables.
  • Deriving test channel distributions to define the Gray and Wyner rate region.
  • Employing canonical correlation coefficients to characterize common information.

Main Results:

  • Demonstrated that Wyner's common information is achieved by a Gaussian random variable of minimum dimension.
  • Provided a formula for common information using canonical correlation coefficients: C(Y1,Y2)=1/2 * sum(log(1+di)/(1-di)).
  • Parameterized rates within the Gray and Wyner rate region and its subsets.

Conclusions:

  • The study provides a deeper understanding of information rates in networks with correlated sources.
  • The findings offer a method to achieve optimal common information using Gaussian variables.
  • The derived rate region parameterization is valuable for network design and analysis.