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 Amazon affiliate links to props: Tetris light: https://amzn.to/3g8BXde Galton Board: https://amzn.to/3gUdLfa Jumbo penny: https://amzn.to/3g8BXde Jumbo quarter: ?? DCI Science Quiz Wal Clock: https://amzn.to/3g8BXde Foam dice: https://amzn.to/3g8BXde TIX LED Clock: https://www.geekalerts.com/tix-led-clock/ Bicycle Playing Cards: https://amzn.to/2E36Na8 Recording in progress door hang sign: https://amzn.to/3la32Av ... https://www.youtube.com/watch?v=xRbrg0P2xv8

A sampling distribution is the distribution of a statistic over samples of the data. Sampling distribution for a normal mean, a t-statistic, and a binomial proportion are discussed. In addition approximate sampling distributions based on the Central Limit Theorem are discussed. 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/I05-Confidence_intervals/Sampling_distribution.pdf 00:25 - Sampling distributions 02:02 - Normal average 03:26 - T-statistic 04:27 - Binomial proportion 06:32 - Central Limit Theorem 07:48 - Approximate sampling distribution for binomial proportion 09:09 - Summary Amazon affiliate links to props: Tetris light: https://amzn.to/3g8BXde Galton Board: https://amzn.to/3gUdLfa Jumbo penny: https://amzn.to/3g8BXde Jumbo quarter: ?? DCI Science Quiz Wal Clock: https://amzn.to/3g8BXde Foam dice: https://amzn.to/3g8BXde TIX LED Clock: https://www.geekalerts.com/tix-led-clock/ Bicycle Playing Cards: https://amzn.to/2E36Na8 Recording in progress door hang sign: https://amzn.to/3la32Av ... https://www.youtube.com/watch?v=1nJ6j9RrIu4

Introduction to Poisson random variables which are used to model counts over time or space with no clear maximum value. A Poisson random variable has a single parameter called the rate parameter which is also the mean and variance of the random variable. Discrete random variables: part 1: https://youtu.be/ajLFqrPTAcY part 2: https://youtu.be/FrL4Dcoy9MI part 3: https://youtu.be/NXUkzZhrrcA part 4: https://youtu.be/cnJjKX5AHi4 STAT 587: https://www.jarad.me/courses/stat587Eng/ Slides: https://www.jarad.me/courses/stat587Eng/slides/Probability/P2-Discrete_distributions/P2-Discrete_distributions.pdf 00:30 - Poisson experiments 01:53 - Poisson random variable 03:12 - New account activation example (Poisson pmf graphic) 04:39 - Poisson probability calculation 06:43 - Sum of independent Poisson random variables 07:44 - Sum of Poisson random variables probability calculation 08:54 - Manufacturing example 10:13 - Poisson approximation to a binomial 11:22 - Proofreading book example 12:26 - Summary (of all parts) Amazon affiliate links to props: Dragonwood: https://amzn.to/3iXy9gY Tetris light: https://amzn.to/3g8BXde Jumbo penny: https://amzn.to/3g8BXde Jumbo quarter: ?? DCI Science Quiz Wal Clock: https://amzn.to/3g8BXde Foam dice: https://amzn.to/3g8BXde TIX LED Clock: https://www.geekalerts.com/tix-led-clock/ Bicycle Play Cards: https://amzn.to/2E36Na8 ... https://www.youtube.com/watch?v=NTWD-EyTkR0

A video about how causal inferential statements can be made about populations. ... https://www.youtube.com/watch?v=lcfyx73cfCc