Bayesian estimation

Bayesian average

A Bayesian average is a method of estimating the mean of a population using outside information, especially a pre-existing belief, which is factored into the calculation. This is a central feature of Bayesian interpretation. This is useful when the available data set is small. Calculating the Bayesian average uses the prior mean m and a constant C. C is chosen based on the typical data set size required for a robust estimate of the sample mean. The value is larger when the expected variation between data sets (within the larger population) is small. It is smaller when the data sets are expected to vary substantially from one another. This is equivalent to adding C data points of value m to the data set. It is a weighted average of a prior average m and the sample average. When the are binary values 0 or 1, m can be interpreted as the prior estimate of a binomial probability with the Bayesian average giving a posterior estimate for the observed data. In this case, C can be chosen based on the desired Binomial proportion confidence interval for the sample value. For example, for rare outcomes when m is small choosing ensures a 99% confidence interval has width about 2m. (Wikipedia).

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36 - Population mean test score - normal prior and likelihood

This video provides an example of Bayesian inference for the case of a normal prior and normal likelihood. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm Unfortunately,

From playlist Bayesian statistics: a comprehensive course

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Bayesian vs frequentist statistics probability - part 1

This video provides an intuitive explanation of the difference between Bayesian and classical frequentist statistics. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm Unfo

From playlist Bayesian statistics: a comprehensive course

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30 - Normal prior and likelihood - known variance

Provides an introduction to the example which will be used to describe inference for the case of a normal likelihood, with known variance, and a normal prior distribution. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com

From playlist Bayesian statistics: a comprehensive course

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35 - Normal prior and likelihood - posterior predictive distribution

This video provides a derivation of the normal posterior predictive distribution for the case of a normal prior distribution and likelihood. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4o

From playlist Bayesian statistics: a comprehensive course

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What is a probability distribution?

An introduction to probability distributions - both discrete and continuous - via simple examples. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm For more information

From playlist Bayesian statistics: a comprehensive course

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Bayesian vs frequentist statistics

This video provides an intuitive explanation of the difference between Bayesian and classical frequentist statistics. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm Un

From playlist Bayesian statistics: a comprehensive course

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What the Heck is Bayesian Stats ?? : Data Science Basics

What's all the hype about Bayesian statistics? My Patreon : https://www.patreon.com/user?u=49277905

From playlist Bayesian Statistics

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Bayesian vs frequentist statistics probability - part 2

This video provides a short introduction to the similarities and differences between Bayesian and Frequentist views on probability. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdi

From playlist Bayesian statistics: a comprehensive course

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39 - The gamma distribution - an introduction

This video provides an introduction to the gamma distribution: describing it mathematically, discussing example situations which can be modelled using a gamma in Bayesian inference, then going on to discuss how its two parameters affect the shape of the distribution intuitively, and finall

From playlist Bayesian statistics: a comprehensive course

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Bayes Billiards with Tom Crawford

Bayes' Theorem allows us to assign a probability to an unknown fact. Thomas Bayes himself described an experiment with a billiard table, which is brilliantly explained by Hannah Fry and Matt Parker here https://www.youtube.com/watch?v=7GgLSnQ48os Brian Cox and David Spiegelhalter did a 1

From playlist Collaborations

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Lecture 10/16 : Combining multiple neural networks to improve generalization

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From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]

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The Surprisingly Effective Magic of Partial Pooling

My Patreon : https://www.patreon.com/user?u=49277905 Partial Pooling Blog Post : https://conductrics.com/prediction-pooling-and-shrinkage 0:00 Intro 7:00 Intuition 9:53 Bayesian Magic Icon References : Coffee shop icons created by smalllikeart - Flaticon https://www.flaticon.com/free-i

From playlist Bayesian Statistics

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Supercharging Decision Making with Bayes

Bayesian Decision Theory is a fundamental statistical approach to the problem of pattern classification. It is considered as the ideal pattern classifier and often used as the benchmark for other algorithms because its decision rule automatically minimizes its loss function. PUBLICATION P

From playlist Machine Learning

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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)

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Statistical Rethinking Fall 2017 - week04 lecture08

Week 04, lecture 08 for Statistical Rethinking: A Bayesian Course with Examples in R and Stan, taught at MPI-EVA in Fall 2017. This lecture covers Chapter 6. Slides are available here: https://speakerdeck.com/rmcelreath Additional information on textbook and R package here: http://xcel

From playlist Statistical Rethinking Fall 2017

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Statistical Learning: 8.6 Bayesian Additive Regression Trees

Statistical Learning, featuring Deep Learning, Survival Analysis and Multiple Testing You are able to take Statistical Learning as an online course on EdX, and you are able to choose a verified path and get a certificate for its completion: https://www.edx.org/course/statistical-learning

From playlist Statistical Learning

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17. Bayesian Statistics

MIT 18.650 Statistics for Applications, Fall 2016 View the complete course: http://ocw.mit.edu/18-650F16 Instructor: Philippe Rigollet In this lecture, Prof. Rigollet talked about Bayesian approach, Bayes rule, posterior distribution, and non-informative priors. License: Creative Commons

From playlist MIT 18.650 Statistics for Applications, Fall 2016

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Why not to be afraid of priors (too much), Paul-Christian Bürkner - Bayes@Lund 2018

More info about Bayes@Lund, including slides: https://bayesat.github.io/lund2018/bayes_at_lund_2018.html

From playlist Bayes@Lund 2018

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Statistical Rethinking - Lecture 08

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From playlist Statistical Rethinking Winter 2015

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How to run A/B Tests as a Data Scientist!

Let's learn about how & why you should use Bayesian Testing. And some advantages of the Bayesian approach over frequentist approach with REAL data/code. Note: Bayesian Appraoch isn't necessarily better in every way - it is another perspective of looking at data. CODE: https://github.com/a

From playlist A/B Testing

Related pages

Binomial proportion confidence interval | Bayesian probability | Mean | Additive smoothing