I3 Bayesian parameter estimation with the binomial model as an example

Bayesian statistics uses Bayes' Rule to make decisions. In the context of a parametric model, parameters are updated from the prior using data to obtain the posterior using Bayes' Rule. From this posterior, Bayes' estimators and credible intervals can be obtained. The video discusses the posterior expectation and equal-tail credible intervals. As an example throughout, the video uses a binomial model with a uniform prior on the probability of success. The posterior is shown (but not derived) to be a beta distribution. A brief detour to discuss the beta distribution ensures. R code is provided to perform all of the Bayesian analyses for binomial data.

Probability playlist: https://www.youtube.com/playlist?list=PLFHD4aOUZFp1FxJs9BG5Sbsy6NvCO3Qb1 Statistics playlist: https://www.youtube.com/playlist?list=PLFHD4aOUZFp1PZC6SgtuS-ESq4ti1GEFj

STAT 587: https://www.jarad.me/courses/stat587Eng/ STAT 587 Videos: https://www.jarad.me/courses/stat587Eng/slides/ Slides: https://www.jarad.me/courses/stat587Eng/slides/Inference/I03-Bayesian_statistics/I03-Bayesian_parameter_estimation.pdf

00:58 - Bayesian statistician 02:24 - Bayes' Rule 04:54 - Bayesian parameter estimation 07:10 - Bayesian notation 08:10 - Binomial model 10:53 - Beta distribution 12:52 - Beta densities 13:42 - Binomial example 15:09 - Posterior density 16:03 - Posterior expectation 17:44 - Credible intervals 19:37 - Credible interval visualization 20:05 - Summary 20:46 - Bayesian analysis for binomial model summary

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