Multivariate Gaussian distributions
Properties of the multivariate Gaussian probability distribution
From playlist cs273a
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
(PP 6.8) Marginal distributions of a Gaussian
For any subset of the coordinates of a multivariate Gaussian, the marginal distribution is multivariate Gaussian.
From playlist Probability Theory
(ML 7.10) Posterior distribution for univariate Gaussian (part 2)
Computing the posterior distribution for the mean of the univariate Gaussian, with a Gaussian prior (assuming known prior mean, and known variances). The posterior is Gaussian, showing that the Gaussian is a conjugate prior for the mean of a Gaussian.
From playlist Machine Learning
(ML 7.9) Posterior distribution for univariate Gaussian (part 1)
Computing the posterior distribution for the mean of the univariate Gaussian, with a Gaussian prior (assuming known prior mean, and known variances). The posterior is Gaussian, showing that the Gaussian is a conjugate prior for the mean of a Gaussian.
From playlist Machine Learning
(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian
An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.
From playlist Probability Theory
(PP 6.10) Sum of independent Gaussians
A sum of independent (multivariate) Gaussians is (multivariate) Gaussian, with mean equal to the sum of the means, and covariance equal to the sum of the covariances.
From playlist Probability Theory
(PP 6.9) Conditional distributions of a Gaussian
For any subset of the coordinates of a multivariate Gaussian, the conditional distribution (given the remaining coordinates) is multivariate Gaussian.
From playlist Probability Theory
Nexus Trimester - Gábor Lugosi (Pompeu Fabra University) 1/2
How to estimate the mean of a random variable? - Part 1 Gábor Lugosi (Pompeu Fabra University) March 14, 2016 Abstract: Given n independent, identically distributed copies of a random variable, one is interested in estimating the expected value. Perhaps surprisingly, there are still open
From playlist 2016-T1 - Nexus of Information and Computation Theory - CEB Trimester
Gábor Lugosi: High-dimensional mean estimation - lecture 2
Recorded during the meeting "Machine learning and nonparametric statistics" the December 15, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio
From playlist Probability and Statistics
Large Deviations for the Largest Eigenvalue of Sub-Gaussian Wigner Matrices by Nicholas Cook
PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab
From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Statistical Rethinking 2023 - 16 - Gaussian Processes
Course: https://github.com/rmcelreath/stat_rethinking_2023 Intro music: https://www.youtube.com/watch?v=_3XGEsDSInM Outline 00:00 Introduction 02:37 Oceanic spatial confounds 09:54 Gaussian processes 24:26 Oceanic Gaussian process 33:51 Pause 34:37 Phylogenetic regression 1:18:39 Summary
From playlist Statistical Rethinking 2023
Stanford CS229: Machine Learning | Summer 2019 | Lecture 9 - Bayesian Methods - Parametric & Non
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3ptRUmB Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html
From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)
2020.05.21 Jason Schweinsberg - A Gaussian particle distribution for branching Brownian motion [...]
A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dime
From playlist One World Probability Seminar
What is the Heisenberg Uncertainty Principle? A wave packet approach
In this video I would like to answer a simple question: according to quantum mechanics, how do you describe a freely moving particle? It sounds simple, but what we will discover is that by attempting to answer this question, we will actually uncover one of the most profound ideas in physic
From playlist Quantum Physics
Statistical Rethinking 2023 - 03 - Geocentric Models
Slides and other materials: https://github.com/rmcelreath/stat_rethinking_2023 Intro music: https://www.youtube.com/watch?v=ayARo_IGV7g Flow: https://www.youtube.com/watch?v=oriuG649ypM Pause: https://www.youtube.com/watch?v=lT5lFeaInl4 Outline 00:00 Introduction 13:56 Gaussian distribut
From playlist Statistical Rethinking 2023
Physics 37.1 Gauss's Law Understood (11 of 29) Spherical Charge Distributions
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the 3 electrical field E1=?, E2=?, and E3=?, at 3 different radii R1, R2, and R3 (inside, at the surface, and outside the surface) of a spherical charge distribution. Next video in this series c
From playlist PHYSICS 37.1 GAUSS'S LAW EXPLAINED
Antonio Lerario: Random algebraic geometry - Lecture 2
CONFERENCE Recording during the thematic meeting : "Real Algebraic Geometry" the October 25, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio
From playlist Algebraic and Complex Geometry
PUSHING A GAUSSIAN TO THE LIMIT
Integrating a gaussian is everyones favorite party trick. But it can be used to describe something else. Link to gaussian integral: https://www.youtube.com/watch?v=mcar5MDMd_A Link to my Skype Tutoring site: dotsontutoring.simplybook.me or email dotsontutoring@gmail.com if you have ques
From playlist Math/Derivation Videos