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# Beginning Bayes in R

This course provides a basic introduction to Bayesian statistics in R.

4 Hours17 Videos56 Exercises

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## Course Description

There are two schools of thought in the world of statistics, the frequentist perspective and the Bayesian perspective. At the core of the Bayesian perspective is the idea of representing your beliefs about something using the language of probability, collecting some data, then updating your beliefs based on the evidence contained in the data. This provides a convenient way of implementing the scientific method for learning about the world we live in. Bayesian statistics is increasingly popular due to recent improvements in computation, the ability to fit a wide range of models, and to produce intuitive interpretations of the results.

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1. 1

### Introduction to Bayesian thinking

Free

This chapter introduces the idea of discrete probability models and Bayesian learning. You'll express your opinion about plausible models by defining a prior probability distribution, you'll observe new information, and then, you'll update your opinion about the models by applying Bayes' theorem.

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Discrete probability distributions
50 xp
Most likely spin?
50 xp
Chance of spinning an even number?
50 xp
Constructing a spinner
100 xp
Simulating spinner data
100 xp
Bayes' rule
50 xp
The prior
50 xp
The likelihoods
50 xp
The posterior
100 xp
Interpreting the posterior
50 xp
Sequential Bayes
50 xp
Bayes with another spin
100 xp
2. 2

### Learning about a binomial probability

This chapter describes learning about a population proportion using discrete and continuous models. You'll use a beta curve to represent prior opinion about the proportion, take a sample and observe the number of successes and failures, and construct a beta posterior curve that combines both the information in the prior and in the sample. You'll then use the beta posterior curve to draw inferences about the population proportion.

3. 3

### Learning about a normal mean

This chapter introduces Bayesian learning about a population mean. You'll sample from a normal population with an unknown mean and a known standard deviation, construct a normal prior to reflect your opinion about the location of the mean before sampling, and see that the posterior distribution also has a normal form with updated values of the mean and standard deviation. You'll also get more practice drawing inferences from the posterior distribution, only this time, about a population mean.

4. 4

### Bayesian comparisons

Suppose you're interested in comparing proportions from two populations. You take a random sample from each population and you want to learn about the difference in proportions. This chapter will illustrate the use of discrete and continuous priors to do this kind of inference. You'll use a Bayesian regression approach to learn about a mean or the difference in means when the sampling standard deviation is unknown.

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Prerequisites

Introduction to RFoundations of Probability in R
Jim Albert

Professor, Bowling Green State University

Jim is Professor of Statistics at Bowling Green State University. His interests include Bayesian thinking, statistics education, statistical computation, and applications of statistics to sports. He is former editor of the Journal of Quantitative Analysis of Sports.
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