Bayesian Statistics: A Step-By-Step Introduction

A former Google data scientist helps you master the basics of Bayesian statistics, with examples in R and Stan

What you'll learn

Understand how Bayes' rule can be used to update beliefs

Use conjugate priors and likelihoods to model binary, count, and continuous data

Understand the concepts of prior distributions, posterior distributions, likelihood functions, and predictive distributions

Understand how statistical software can be used to compute and visualize information about your beliefs

Requirements

Strong skills in basic algebra and arithmetic

Some knowledge of calculus is useful, but not required.

Description

This course teaches the foundational material of statistics covered in an introductory college course, with a focus on mastering the basic components of any Bayesian model - the prior distribution and the likelihood, and how to find a posterior distribution, credible intervals, and predictive distributions.  Along the way, you'll become more comfortable with probability in general and gain a new perspective on how to analyze data!We start from scratch - no experience in Bayesian statistics is required.  Students should have a strong grasp of basic algebra and arithmetic.  R and RStudio, or Python, is required if you would like to run the optional coding sectionsThe course includes:5.5 hours of video lecturesInteractive demonstrations using R and Stan (Python code is included too!)Quizzes to check your understandingReview assignments with solutions to practice what you have learnedYou will learn:The basic rules of probabilityBayes' rule, including common examples with medical testing and flipping coinsThe terminology of different components of a Bayesian model: the prior distribution, posterior, likelihood, and predictive distributionConjugate priorsCredible intervals and Bayes estimatorsModeling binary data with the Bernoulli and Binomial Distribution, and the Beta distribution priorModeling count data with the Poisson Distribution, and the Gamma distribution priorModeling continuous data with the Normal Distribution, and the Normal distribution priorAn introduction to simple linear regressionThis course is ideal for many types of students:Anyone who wants to learn the foundations of Bayesian statistics and understand concepts like priors, posteriors and credible intervalsData science and data analytics professionals who would like to refresh and expand their statistics knowledgeAcademics in the social, biological, and physical sciencesThis course is ideal for anyone, from beginners to seasoned professionals. It doesn't matter if you're just starting your journey in data science, looking to upgrade your existing skills, or simply have an interest in Bayesian statistics. My goal is to make Bayesian statistics accessible and understandable for all.

Overview

Section 1: Probability Basics

Lecture 1 Introduction Video

Lecture 2 Welcome

Lecture 3 Probability, Complements, Venn Diagrams

Lecture 4 Law of Total Probability

Lecture 5 Conditional Probability

Lecture 6 Multiplication Rule and Independence

Lecture 7 Probability Extra Practice Problems

Section 2: Bayes' Rule

Lecture 8 Bayes' Rule Introduction

Lecture 9 Medical Testing Problem

Lecture 10 Predictive Distributions and Flow Charts

Lecture 11 Two Coins

Lecture 12 Multiple Observations

Lecture 13 Normalizing Constants and Proportionality

Lecture 14 Bayes' Rule Extra Practice Problems

Section 3: Continuous Priors and the Uniform Distribution

Lecture 15 Continuous Priors and the Uniform Distribution

Lecture 16 Likelihood and Random Variables

Lecture 17 Posterior Distribution: One Observation

Lecture 18 Posterior Probability Calculation

Lecture 19 Posterior Distribution: Two Observations

Lecture 20 CDFs and Inverse CDFs

Lecture 21 Credible Intervals

Lecture 22 Mean, Median, Mode

Lecture 23 Point Estimates

Lecture 24 Predictive Distribution

Section 4: Beta-Binomial Family

Lecture 25 Binomial Random Variables

Lecture 26 Prior: The Beta Distribution

Lecture 27 Finding prior and posterior probabilities with the Beta CDF

Lecture 28 How do the hyperparameters change the prior?

Lecture 29 Posterior Distribution: What are Conjugate Priors?

Lecture 30 Credible Intervals

Lecture 31 Point Estimates

Lecture 32 Predictive Distribution: Beta-Binomial

Lecture 33 Recap of Priors, Posteriors, Likelihoods, Predictive Distributions

Lecture 34 Example Beta-Binomial Problem with R

Lecture 35 Example Beta-Binomial Problem with Stan

Lecture 36 Drawbacks of Conjugate Priors

Section 5: Poisson - Gamma

Lecture 37 Likelihood: Poisson Distribution

Lecture 38 Gamma Distribution and Choosing Hyperparameters

Lecture 39 Posterior Distribution

Lecture 40 Posterior Calculation Example 2

Lecture 41 Credible Interval and Point Estimates

Lecture 42 Predictive Distribution: Negative Binomial

Lecture 43 Example Poisson-Gamma Problem with R and Stan

Section 6: Normal - Normal

Lecture 44 Normal Distribution

Lecture 45 Prior: Normal Distribution and choosing hyperparameters

Lecture 46 Posterior Distribution and Example

Lecture 47 Credible Intervals and Point Estimates

Lecture 48 Example Normal-Normal Problem with R and Stan

Section 7: More advanced models

Lecture 49 Predictive distributions, unknown variance

Lecture 50 Simple Linear Regression

Lecture 51 Example Simple Linear Regression Problem with R and Stan

Current and aspiring data scientists and data analysts,Academics in the social, biological, and physical sciences,University students studying mathematics or statistics,Anybody who wants to learn to rigorously update their beliefs from data.