In astronomy, a correlation function describes the distribution of galaxies in the universe. By default, "correlation function" refers to the two-point autocorrelation function. The two-point autocorrelation function is a function of one variable (distance); it describes the excess probability of finding two galaxies separated by this distance (excess over and above the probability that would arise if the galaxies were simply scattered independently and with uniform probability). It can be thought of as a clumpiness factor - the higher the value for some distance scale, the more clumpy the universe is at that distance scale. The following definition (from Peebles 1980) is often cited: Given a random galaxy in a location, the correlation function describes the probability that another galaxy will be found within a given distance. However, it can only be correct in the statistical sense that it is averaged over a large number of galaxies chosen as the first, random galaxy. If just one random galaxy is chosen, then the definition is no longer correct, firstly because it is meaningless to talk of just one "random" galaxy, and secondly because the function will vary wildly depending on which galaxy is chosen, in contradiction with its definition as a function. Assuming the universe is isotropic (which observations suggest), the correlation function is a function of a scalar distance. The two-point correlation function can then be written as where is a unitless measure of overdensity, defined at every point. Letting , it can also be expressed as the integral The spatial correlation function is related to the Fourier space power spectrum of the galaxy distribution, , as The n-point autocorrelation functions for n greater than 2 or cross-correlation functions for particular object types are defined similarly to the two-point autocorrelation function. The correlation function is important for theoretical models of physical cosmology because it provides a means of testing models which assume different things about the contents of the universe. (Wikipedia).
Teach Astronomy - Causation and Correlation
http://www.teachastronomy.com/ Science starts by looking for patterns in data. Therefore it's important to understand the distinction between causation and correlation. Scientists believe in causation, the general idea that events have causes. However science starts by looking for patte
From playlist 01. Fundamentals of Science and Astronomy
From playlist Courses and Series
Ken McLaughlin: Correlation functions for some integrable systems with random initial... - Lecture 2
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From playlist Probability and Statistics
From playlist Courses and Series
This video explains how to find the correlation coefficient which describes the strength of the linear relationship between two variables x and y. My Website: https://www.video-tutor.net Patreon: https://www.patreon.com/MathScienceTutor Amazon Store: https://www.amazon.com/shop/theorga
From playlist Statistics
Tamara Grava: Correlation functions for some integrable systems with random initial... - Lecture 1
Title: Correlation functions for some integrable systems with random initial data, theory and computation - Lecture 1 Abstract: We will investigate the form of spatio-temporal correlation functions for integrable models of systems of particles on the line. There are few analytical results
From playlist Probability and Statistics
Covariance Definition and Example
What is covariance? How do I find it? Step by step example of a solved covariance problem for a sample, along with an explanation of what the results mean and how it compares to correlation. 00:00 Overview 03:01 Positive, Negative, Zero Correlation 03:19 Covariance for a Sample Example
From playlist Correlation
RELATIONSHIPS Between Variables: Standardized Covariance (7-1)
Correlation is a way of measuring the extent to which two variables are related. The term correlation is synonymous with “relationship.” Variables are related when changes in one variable are consistently associated with changes in another variable. Dr. Daniel reviews Variance, Covariance,
From playlist Correlation And Regression in Statistics (WK 07 - QBA 237)
Limits of correlation (applied)
Correlation is a standardized covariance (i.e., translated into unit-less form with volatilities). It cannot be used alone: (i) it can be "distorted" by low volatilities, and (ii) it does not give information revealed by the scatter (in this example, both hedge fund series are similarly co
From playlist Statistics: Introduction
GRCon21 - GNU Radio at the Allen Telescope Array
Presented by Michael Piscopo at GNU Radio Conference 2021 Through a community partnership between GNU Radio and the ATA, a project to create a fully functional radio astronomy X-Engine based on GNU Radio and high-end GPU's has been in progress to support science observations at the telesc
From playlist GRCon 2021
Cosmology with Gravitational Waves (Lecture 1) by Archisman Ghosh
Program Cosmology - The Next Decade ORGANIZERS : Rishi Khatri, Subha Majumdar and Aseem Paranjape DATE : 03 January 2019 to 25 January 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The great observational progress in cosmology has revealed some very intriguing puzzles, the most i
From playlist Cosmology - The Next Decade
The Physical, statistical, and computational challenges of Pulsar Timing by Justin Ellis
20 March 2017 to 25 March 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru This joint program is co-sponsored by ICTS and SAMSI (as part of the SAMSI yearlong program on Astronomy; ASTRO). The primary goal of this program is to further enrich the international collaboration in the area
From playlist Time Series Analysis for Synoptic Surveys and Gravitational Wave Astronomy
Transient noise in the LIGO detectors by Jessica Mclver
20 March 2017 to 25 March 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru This joint program is co-sponsored by ICTS and SAMSI (as part of the SAMSI yearlong program on Astronomy; ASTRO). The primary goal of this program is to further enrich the international collaboration in the area
From playlist Time Series Analysis for Synoptic Surveys and Gravitational Wave Astronomy
PSD, Structure Function, and CARMA Analysis of AGN Variability by Jackeline Moreno
20 March 2017 to 25 March 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru This joint program is co-sponsored by ICTS and SAMSI (as part of the SAMSI yearlong program on Astronomy; ASTRO). The primary goal of this program is to further enrich the international collaboration in the area
From playlist Time Series Analysis for Synoptic Surveys and Gravitational Wave Astronomy
Jocelyn Read - Gravitational-wave observations of neutron-star mergers - IPAM at UCLA
Recorded 18 November 2021. Jocelyn Read of California State University, Fullerton (CSU Fullerton) presents " Gravitational-wave observations of neutron-star mergers" at IPAM's Workshop III: Source inference and parameter estimation in Gravitational Wave Astronomy. Abstract: New discoverie
From playlist Workshop: Source inference and parameter estimation in Gravitational Wave Astronomy
Observations of gravitational-wave from a binary neutron star inspiral by Parameswaran Ajith
Date and Time: 19 October 2017, 10:00 - 13:00 Venue: Ramanujan Lecture Hall, ICTS Bangalore The recent detection of gravitational waves from a merging binary neutron star system, along with follow-up observations in the full frequency band of the electromagnetic spectrum mark the dawn o
From playlist Cosmic Fireworks: The Dawn Of Multimessenger Astronomy
Causation and Correlation | Introductory Astronomy Course 1.06
Welcome to Astronomy: Exploring Time and Space, a course from Professor Impey, a University Distinguished Professor of Astronomy at the University of Arizona. Learn about the foundations of astronomy in this free online course here on YouTube. This video is part of module 1, Science and Hi
From playlist Introductory Astronomy Module 1: Science and History
Reasoning and Uncertainty | History and Philosophy of Astronomy 2.05
Learn about the history and philosophy of astronomy from Professor Impey, a University Distinguished Professor of Astronomy at the University of Arizona, with our Knowing the Universe: History and Philosophy of Astronomy course here on YouTube. This video is part of module 2, Greek Science
From playlist History and Philosophy Course Module 2: Greek Science
Teach Astronomy - Galaxy Luminosity Function
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From playlist 20. Galaxy Interaction and Motion
Formation and evolution of compact binaries (Lecture - 02) by Tomasz Bulik
Summer School on Gravitational-Wave Astronomy DATE: 17 July 2017 to 28 July 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore This school is a part of the annual ICTS summer schools in gravitational wave astronomy. This year’s school will focus on the physics and astrophysics of compact
From playlist Summer School on Gravitational-Wave Astronomy - 2017