Exponential family distributions | Multivariate continuous distributions | Continuous distributions | Conjugate prior distributions
In statistics, the inverted Dirichlet distribution is a multivariate generalization of the beta prime distribution, and is related to the Dirichlet distribution. It was first described by Tiao and Cuttman in 1965. The distribution has a density function given by The distribution has applications in statistical regression and arises naturally when considering the multivariate Student distribution. It can be characterized by its mixed moments: provided that and . The inverted Dirichlet distribution is conjugate to the negative multinomial distribution if a generalized form of odds ratio is used instead of the categories' probabilities. T. Bdiri et al. have developed several models that use the inverted Dirichlet distribution to represent and model non-Gaussian data. They have introduced finite and infinite mixture models of inverted Dirichlet distributions using the Newton–Raphson technique to estimate the parameters and the Dirichlet process to model infinite mixtures. T. Bdiri et al. have also used the inverted Dirichlet distribution to propose an approach to generate Support Vector Machine kernels basing on Bayesian inference and another approach to establish hierarchical clustering. (Wikipedia).
(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
Value distribution of long Dirichlet polynomials and applications to the Riemann...-Maksym Radziwill
Maksym Radziwill Value distribution of long Dirichlet polynomials and applications to the Riemann zeta-function Stanford University; Member, School of Mathematics October 1, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Determining values of a variable at a particular percentile in a normal distribution
From playlist Unit 2: Normal Distributions
(ML 7.8) Dirichlet-Categorical model (part 2)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
(ML 7.7) Dirichlet-Categorical model (part 1)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals
The Normal Distribution (1 of 3: Introductory definition)
More resources available at www.misterwootube.com
From playlist The Normal Distribution
Lecture 23: The Dirichlet Problem on an Interval
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=QTg7040uSc0&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Using normal distribution to find the probability
👉 Learn how to find probability from a normal distribution curve. A set of data are said to be normally distributed if the set of data is symmetrical about the mean. The shape of a normal distribution curve is bell-shaped. The normal distribution curve is such that the mean is at the cente
From playlist Statistics
Calderon problem (Lecture 1) by Venkateswaran P Krishnan
DISCUSSION MEETING WORKSHOP ON INVERSE PROBLEMS AND RELATED TOPICS (ONLINE) ORGANIZERS: Rakesh (University of Delaware, USA) and Venkateswaran P Krishnan (TIFR-CAM, India) DATE: 25 October 2021 to 29 October 2021 VENUE: Online This week-long program will consist of several lectures by
From playlist Workshop on Inverse Problems and Related Topics (Online)
Geometric inverse problems (Lecture - 2) by Gunther Uhlmann
DISCUSSION MEETING WORKSHOP ON INVERSE PROBLEMS AND RELATED TOPICS (ONLINE) ORGANIZERS: Rakesh (University of Delaware, USA) and Venkateswaran P Krishnan (TIFR-CAM, India) DATE: 25 October 2021 to 29 October 2021 VENUE: Online This week-long program will consist of several lectures by
From playlist Workshop on Inverse Problems and Related Topics (Online)
Learn how to create a normal distribution curve given mean and standard deviation
👉 Learn how to find probability from a normal distribution curve. A set of data are said to be normally distributed if the set of data is symmetrical about the mean. The shape of a normal distribution curve is bell-shaped. The normal distribution curve is such that the mean is at the cente
From playlist Statistics
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Topic Models: Variational Inference for Latent Dirichlet Allocation (with Xanda Schofield)
This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://sites.google.com/umd.edu/2021cl1webpage/ (Including homeworks and reading.) Xanda's Webpage: https://www.cs.hmc.edu/~xanda
From playlist Computational Linguistics I
(ML 8.5) Bayesian Naive Bayes (part 3)
When all the features are categorical, a naïve Bayes classifier can be made fully Bayesian by putting Dirichlet priors on the parameters and (exactly) integrating them out.
From playlist Machine Learning
Stochastic Homogenization (Lecture 3) by Andrey Piatnitski
DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Daniel Slonim (Purdue) -- Random Walks in Dirichlet Random Environments on Z with Bounded Jumps
Random walks in random environments (RWRE) are well understood in the one-dimensional nearest-neighbor case. A surprising phenomenon is the existence of models where the walk is transient to the right, but with zero limiting velocity. More difficulties are presented by nearest-neighbor RWR
From playlist Northeastern Probability Seminar 2021
From playlist Contributed talks One World Symposium 2020
Why do prime numbers make these spirals? | Dirichlet’s theorem, pi approximations, and more
A curious pattern, approximations for pi, and prime distributions. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/spiral-thanks Based on this Math
From playlist Neat proofs/perspectives
Statistics: Ch 7 Sample Variability (3 of 14) The Inference of the Sample Distribution
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 if the number of samples is greater than or equal to 25 then: 1) the distribution of the sample means is a normal distr
From playlist STATISTICS CH 7 SAMPLE VARIABILILTY