Discrete distributions | Statistical approximations
The Kirkwood superposition approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution. The Kirkwood approximation for a discrete probability density function is given by where is the product of probabilities over all subsets of variables of size i in variable set . This kind of formula has been considered by Watanabe (1960) and, according to Watanabe, also by Robert Fano. For the three-variable case, it reduces to simply The Kirkwood approximation does not generally produce a valid probability distribution (the normalization condition is violated). Watanabe claims that for this reason informational expressions of this type are not meaningful, and indeed there has been very little written about the properties of this measure. The Kirkwood approximation is the probabilistic counterpart of the interaction information. Judea Pearl (1988 §3.2.4) indicates that an expression of this type can be exact in the case of a decomposable model, that is, a probability distribution that admits a graph structure whose cliques form a tree. In such cases, the numerator contains the product of the intra-clique joint distributions and the denominator contains the product of the clique intersection distributions. (Wikipedia).
Polynomial approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Using Taylor Polynomials to Approximate Functions
This video shows how to determine a Taylor Polynomial to approximate a function. http://mathispower4u.yolasite.com/
From playlist Infinite Sequences and Series
Approximating Functions in a Metric Space
Approximations are common in many areas of mathematics from Taylor series to machine learning. In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space. Chapters 0:00 - Examples of Approximation 0:46 - Best Aproximati
From playlist Approximation Theory
Error bounds for Taylor approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Midpoint riemann sum approximation
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Intro to Taylor Series: Approximations on Steroids
While in Calc I we used Linear Approximations, can we approximate functions by quadratics, cubics, etc? Indeed, Taylor Series (and Maclauren series when they are centered at x=0) provide a method for effective approximation of functions locally. And the best part is all we need to know is
From playlist Calculus II (Integration Methods, Series, Parametric/Polar, Vectors) **Full Course**
Teach Astronomy - Kirkwood Gaps
http://www.teachastronomy.com/ Although most asteroids in the main belt are found at distances between two and three astronomical units from the Sun, their distribution with radius is neither random nor uniform. Structure in the asteroid belt radially was discovered by Daniel Kirkwood the
From playlist 11. Interplanetary Bodies
Classical and Quantum Subjectivity
Uncertainty is a major component of subjective logic beliefs. We discuss the cloud of uncertainty across Markov networks, insights from computational irreducibility, and negative quantum quasiprobabilities and beliefs.
From playlist Wolfram Technology Conference 2022
Twitch Talks - Astronomy & Space Entities
Presenter: Jeff Bryant Wolfram Research developers demonstrate the new features of Version 12 of the Wolfram Language that they were responsible for creating. Previously broadcast live on July 9, 2019 at twitch.tv/wolfram. For more information, visit: https://www.wolfram.com/language/12/a
From playlist Twitch Talks
Stanford Law School memorial pays tribute to WWII veterans
During a full military ceremony, complete with an honor guard and music by the U.S. Air Force’s Band of the Golden West, the center of attention was a large bronze plaque that was recently unearthed in a basement storeroom at the law school. On it are the names of 18 Stanford Law School al
From playlist Stanford Highlights
Why Isn't the Asteroid Belt a Planet?
It seems like there's a strange gap in between Mars and Jupiter filled with rocky rubble. Why didn't the asteroid belt form into a planet, like the rest of the Solar System?
From playlist The Solar System
Polynomial approximation of functions (part 1)
Using a polynomial to approximate a function at f(0). More free lessons at: http://www.khanacademy.org/video?v=sy132cgqaiU
From playlist Calculus
Entropy production and phoretic transport (Lecture 3) by Daan Frenkel
INFOSYS-ICTS CHANDRASEKHAR LECTURES FROM SELF-ASSEMBLY TO CELL RECOGNITION Daan Frenkel (University of Cambridge, UK) DATE :29 August 2018, 16:00 to 17:00 VENUE:Ramanujan Lecture Hall, ICTS Bangalore. Lecture 1: Tuesday 28 August, 16:00 to 17:00 Title : Order, disorder and entropy Ab
From playlist Infosys-ICTS Chandrasekhar Lectures
Right hand riemann sum approximation
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Kurt Kremer: Multiscale modeling for soft matter - Perspectives and challenges
Abstract: Material properties of soft matter are governed by a delicate interplay of energetic and entropic contributions. In other words, generic universal aspects are as relevant as local chemistry specific properties. Thus many different time and length scales are intimately coupled, wh
From playlist Numerical Analysis and Scientific Computing
Comment Responses: Are 400+ TV Shows Happening In The Same Universe? | PBS Digital Studios
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateidea Tweet us! http://bit.ly/pbsideachanneltwitter Idea Channel Facebook! http://bit.ly/pbsideachannelfacebook Talk about this episode on reddit! http://bit.ly/pbsideachanne
From playlist Comment Responses!
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
Asteroids: Crash Course Astronomy #20
Now that we’ve finished our tour of the planets, we’re headed back to the asteroid belt. Asteroids are chunks of rock, metal, or both that were once part of smallish planets but were destroyed after collisions. Most orbit the Sun between Mars and Jupiter, but some get near the Earth. The b
From playlist Astronomy
Accuracy of Taylor approximations - Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Featuring Andrea Hawksley, Gordon Kirkwood, and Watz. This is the result of pulling back the spherical video (seen as a textured Riemann sphere) by a degree five rational function. I carefully chose the positions of the branch points to make the scene unwrap in an interesting way. Raw f
From playlist Spherical video