Bayesian statistics | Conjugate prior distributions

Conjugate prior

In Bayesian probability theory, if the posterior distribution is in the same probability distribution family as the prior probability distribution , the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function . A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary. Further, conjugate priors may give intuition by more transparently showing how a likelihood function updates a prior distribution. The concept, as well as the term "conjugate prior", were introduced by Howard Raiffa and Robert Schlaifer in their work on Bayesian decision theory. A similar concept had been discovered independently by George Alfred Barnard. (Wikipedia).

Video thumbnail

(ML 7.4) Conjugate priors

Definition of conjugate priors, and a couple of examples. For more detailed examples, see the videos on the Beta-Bernoulli model, the Dirichlet-Categorical model, and the posterior distribution of a univariate Gaussian.

From playlist Machine Learning

Video thumbnail

What is the complex conjugate?

What is the complex conjugate of a complex number? Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook

From playlist Intro to Complex Numbers

Video thumbnail

Conjugate of products is product of conjugates

For all complex numbers, why is the conjugate of two products equal to the product of their conjugates? Basic example is discussed. Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook

From playlist Intro to Complex Numbers

Video thumbnail

Calculations with the complex conjugate

How to perform calculations with the complex conjugate. Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook

From playlist Intro to Complex Numbers

Video thumbnail

17 - Conjugate priors - an introduction

This video provides a short introduction to the concept of 'conjugate prior distributions'; covering its definition, examples and why we may choose to specify a distribution that is conjugate to a given likelihood. If you are interested in seeing more of the material, arranged into a play

From playlist Bayesian statistics: a comprehensive course

Video thumbnail

Calculus 2: Complex Numbers & Functions (8 of 28) Conjugate Rules 1 and 2

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and show numerically that the sum and product of the conjugate are the sums and products of its conjugates, rules 1 and 2. Next video in the series can be seen at: https://youtu.be/QsalK_U5Lm

From playlist CALCULUS 2 CH 11 COMPLEX NUMBERS

Video thumbnail

Ex: Multiplying Complex Conjugates

This video defines complex conjugates and provides and example of how to determine the product of complex conjugates. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com

From playlist Performing Operations with Complex Numbers

Video thumbnail

Conjugates

Conjugates are very useful.

From playlist Algebra

Video thumbnail

Bayesian Statistics: An Introduction

See all my videos here: http://www.zstatistics.com/videos/ 0:00 Introduction 2:25 Frequentist vs Bayesian 5:55 Bayes Theorum 10:45 Visual Example 15:05 Bayesian Inference for a Normal Mean 24:30 Conjugate priors 32:55 Credible Intervals

From playlist Statistical Inference (7 videos)

Video thumbnail

Complex conjugate and linear systems

How to solve linear systems with the complex conjugate. Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook

From playlist Intro to Complex Numbers

Video thumbnail

Kerrie Mengersen: Bayesian Modelling

Abstract: This tutorial will be a beginner’s introduction to Bayesian statistical modelling and analysis. Simple models and computational tools will be described, followed by a discussion about implementing these approaches in practice. A range of case studies will be presented and possibl

From playlist Probability and Statistics

Video thumbnail

20 - Beta conjugate prior to Binomial and Bernoulli likelihoods

This video sketches a short proof of the fact that a Beta distribution is conjugate to both Binomial and Bernoulli likelihoods. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB

From playlist Bayesian statistics: a comprehensive course

Video thumbnail

41 - Proof: Gamma prior is conjugate to Poisson likelihood

This video provides a proof of the fact that a Gamma prior distribution is conjugate to a Poisson likelihood function. If you are interested in seeing more of the material on Bayesian statistics, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4

From playlist Bayesian statistics: a comprehensive course

Video thumbnail

Bayesian statistics syllabus

A description of the syllabus that will be covered in this course on Bayesian statistics. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm Unfortunately, Ox Educ is no m

From playlist Bayesian statistics: a comprehensive course

Video thumbnail

Stanford CS234: Reinforcement Learning | Winter 2019 | Lecture 12 - Fast Reinforcement Learning II

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/ai Professor Emma Brunskill, Stanford University http://onlinehub.stanford.edu/ Professor Emma Brunskill Assistant Professor, Computer Science Stanford AI for Hu

From playlist Stanford CS234: Reinforcement Learning | Winter 2019

Video thumbnail

ML Tutorial: Probabilistic Numerical Methods (Jon Cockayne)

Machine Learning Tutorial at Imperial College London: Probabilistic Numerical Methods Jon Cockayne (University of Warwick) February 22, 2017

From playlist Machine Learning Tutorials

Video thumbnail

Complex Conjugate Root Theorem (2 of 2: Other conjugate properties)

More resources available at www.misterwootube.com

From playlist Using Complex Numbers

Video thumbnail

Jason Parker - Covariant Isotropy of Grothendieck Toposes

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/ParkerSlidesToposesOnline.pdf Covariant isotropy can be regarded as providing an abstract notion of conjugation or i

From playlist Toposes online

Related pages

Numerical integration | Exponential family | Bayes' theorem | Inverse-Wishart distribution | Beta distribution | Posterior predictive distribution | Hypergeometric distribution | Dynamical system | Dirichlet distribution | Gamma distribution | Probability density function | Exchangeable random variables | Inverse-gamma distribution | Exponential distribution | Covariance matrix | Weibull distribution | Multivariate normal distribution | Recursive Bayesian estimation | Order of magnitude | Hyperprior | Bernoulli trial | Lomax distribution | Dirichlet-multinomial distribution | Pareto distribution | Poisson distribution | Scaled inverse chi-squared distribution | Howard Raiffa | Log-normal distribution | Robert Schlaifer | Posterior probability | Maximum likelihood estimation | Closed-form expression | Beta negative binomial distribution | Likelihood function | Normal-Wishart distribution | List of probability distributions | Multinomial distribution | Bayesian probability | Convex combination | Normal distribution | Hyperparameter | Linear combination | Beta function | Negative binomial distribution | Geometric distribution | Operator theory | Random variable | Normal-gamma distribution | Normal-inverse-Wishart distribution | Binomial distribution | Beta-binomial distribution | Wishart distribution | Data assimilation | Categorical distribution | Probability mass function | Bernoulli distribution