(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
(PP 6.2) Multivariate Gaussian - examples and independence
Degenerate multivariate Gaussians. Some sketches of examples and non-examples of Gaussians. The components of a Gaussian are independent if and only if they are uncorrelated.
From playlist Probability Theory
(PP 6.6) Geometric intuition for the multivariate Gaussian (part 1)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
(PP 6.7) Geometric intuition for the multivariate Gaussian (part 2)
How to visualize the effect of the eigenvalues (scaling), eigenvectors (rotation), and mean vector (shift) on the density of a multivariate Gaussian.
From playlist Probability Theory
Introductory Probability Theory
A video introducing and deriving the foundations of probability theory up until the law of total probability and Bayes' theorem. This is an entry to the Summer of Math Exposition held by @3blue1brown. #SoME2 #3b1b #probability
From playlist Summer of Math Exposition 2 videos
Statistics: Ch 4 Probability in Statistics (20 of 74) Definition of Probability
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the “strict” definition of experimental (empirical) and theoretical probability. Next video in this series can be seen
From playlist STATISTICS CH 4 STATISTICS IN PROBABILITY
What Is Probability? Difficulties Understanding Probability
Professor David Wallace discusses the nature of probability and some of the philosophical puzzles that arise regarding how to understand and make sense of probability. He begins by distinguishing between subjective probabilities (which are about our beliefs) and objective probabilities (wh
From playlist Logic & Philosophy of Mathematics
(PP 6.4) Density for a multivariate Gaussian - definition and intuition
The density of a (multivariate) non-degenerate Gaussian. Suggestions for how to remember the formula. Mathematical intuition for how to think about the formula.
From playlist Probability Theory
A Friendly Introduction to Rigorous Probability Theory || Chapter 1, Probability Spaces
Here, I talk about why a rigorous (measure theoretic) framework for probability theory is needed, and also give an intuitive idea of various abstract ideas in rigorous probability such as sigma-algebras and the axioms of probability. This is my contribution to Grant Sanderson's (3blue1brow
From playlist Summer of Math Exposition Youtube Videos
A surprising majorization relation and its applications - N. Datta - Main Conference - CEB T3 2017
Nilanjana Datta (Cambridge) / 11.12.2017 Title: A surprising majorization relation and its applications Abstract: Any two arbitrary quantum states, acting on a given Hilbert space, need not be related by a majorization ordering, even if they are close to each other. Surprisingly, howeve
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Random Products and Quantum Simulation by Joel Tropp
PROGRAM: ADVANCES IN APPLIED PROBABILITY II (ONLINE) ORGANIZERS: Vivek S Borkar (IIT Bombay, India), Sandeep Juneja (TIFR Mumbai, India), Kavita Ramanan (Brown University, Rhode Island), Devavrat Shah (MIT, US) and Piyush Srivastava (TIFR Mumbai, India) DATE: 04 January 2021 to 08 Januar
From playlist Advances in Applied Probability II (Online)
Math Major Guide | Warning: Nonstandard advice.
A guide for how to navigate the math major and how to learn the main subjects. Recommendations for courses and books. Comment below to tell me what you think. And check out my channel for conversation videos with guests on math and other topics: https://www.youtube.com/channel/UCYLOc-m8Wu
From playlist Math
An introductory survey on expanders and their applications - Avi Wigderson
Computer Science/Discrete Mathematics Seminar II Topic: An introductory survey on expanders and their applications Speaker: Avi Wigderson Affiliation: Herbert H. Maass Professor, School of Mathematics Date: September 29, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Shannon 100 - 26/10/2016 - Mérouane DEBBAH
Random Matrices and Telecommunications Mérouane Debbah (CentraleSupélec et Huawei France R&D) The asymptotic behaviour of the eigenvalues of large random matrices has been extensively studied since the fifties. One of the first related result was the work of Eugène Wigner in 1955 who rem
From playlist Shannon 100
ICM 2006 Closing Round Table Are pure and applied mathematics drifting apart? Intervention by John Ball (Slides https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/tars/table2006_ball.pdf) Intervention by Lennart Carleson (Slides https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/
From playlist Number Theory
The Abel Prize announcement 2020 — Hillel Furstenberg & Gregory Margulis
0:50 The Abel Prize announced by Hans Petter Graver, President of The Norwegian Academy of Science and Letters 1:37 Citation by Hans Munthe-Kaas, Chair of the Abel committee 9:28 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 16:21 I
From playlist Gregory Margulis
Nexus Trimester - Ioannis Kontoyiannis (Athens U of Econ & Business)
Testing temporal causality and estimating directed information Ioannis Kontoyiannis (Athens U of Econ & Business) March 18, 2016 Abstract: The problem of estimating the directed information rate between two Markov chains of arbitrary (but finite) order is considered. Specifically for the
From playlist 2016-T1 - Nexus of Information and Computation Theory - CEB Trimester
Yakov Sinai: Now everything has been started? The origin of deterministic chaos
Abstract: The theory of deterministic chaos studies statistical properties of solutions of non-linear equations and has many applications. The appearance of these properties is connected with intrinsic instability of dynamics. This lecture was held by Abel Laureate Yakov Grigorevich Sina
From playlist Abel Lectures
(PP 1.4) Measure theory: Examples of Measures
Some examples of probability measures. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4 You can skip the measure theory (Section 1) if you're not interested in the rigorous underpinnings. If you choose to do th
From playlist Probability Theory
Jean-François Quint - 5/6 Mesures stationnaires et fermés invariants des espaces homogènes
Dans ce cours, je présenterai des résultats que j'ai obtenus récemment en collaboration avec Yves Benoist. Nous avons démontré que, pour certaines actions de groupes sur des espaces homogènes, les adhérences d'orbites sont toutes des sous-variétés. Cet énoncé fait suite à de célèbres trava
From playlist Jean-François Quint - Mesures stationnaires et fermés invariants des espaces homogènes