1. Welcome to the course!
Hi and welcome to this course on the fundamentals of Bayesian data analysis using R.
2. This is me
And here's me, Rasmus Bååth, Data scientists and Bayesian enthusiast. I'll be your guide on your journey through this course. Let's get started!
3. WW2 naval scene
In 1941 the British made a breakthrough in the war against Nazi Germany. During the beginning of the war, the German forces had been using a purpose-built typewriter,
4. The Enigma machine
the Enigma machine, to encrypt military communication. But in 1941 a British team spearheaded by computer scientist
5. Alan Turing
Alan Turing finally designed a method that could decrypt German communication, and needless to say, this gave the allied powers a huge advantage in war.
The reason I start out a course on Bayesian data analysis with a story from the second world war is that a key to Alan Turing's success in cracking the Enigma code was his use of Bayesian methods. At the time, Bayesian methods were not widely used
6. Bayesian montage
but nowadays they are used in everything from AB-testing and statistical modeling to machine learning and robotics.
7. Bayesian inference in a nutshell
In a nutshell, what is Bayesian inference?
Bayesian inference is a method for figuring out unknown or unobservable quantities given known facts. There are other inference methods for this, but what makes Bayesian inference Bayesian is that it uses probability to describe the uncertainty over what the values of the unknown quantities could be.
In the case of the Enigma Machine, the unknown quantity Alan Turing wanted to figure out was
8. The Enigma machine with wheels
the configuration of these three wheels. The person encrypting the message selected these wheels from a pool of eight different wheels and their position defined how messages were encrypted. But if you're not the person who encrypted the message you don't know which wheels were used and what positions they had. The British had a working model for
9. Enigma model
how specific wheel settings produced encrypted messages, but really wanted to figure out the opposite: Given these secret messages, what was likely the settings of the wheels that produced them? Alan Turing's solution was to use
10. Enigma model with Bayesian inference
Bayesian inference to work backward from the encrypted messages to arrive at the probable setting of the wheels.
11. Bayesian data analysis
Bayesian Data analysis is then the use of Bayesian inference to learn from data, the known facts, and the unknown quantities we want to learn about are the values of parameters or what future data might look like. Bayesian data analysis is a broadly useful approach and there are Bayesian versions of common statistical procedures such as hypothesis testing and linear regression. But the real power of Bayesian data analysis is its flexibility and that it allows you to construct problem specific models that can make the best use of your data.
12. Course overview
In this first chapter of the course, you'll get to do some Bayesian data analysis yourself. You'll get run a small Bayesian analysis from start to finish, but we'll go light on the theory. We'll save that for chapter two, three and four where we will get to the bottom of how Bayesian inference really works. Look at some reasons why you would want to use Bayesian data analysis. And learn what Bayes theorem is all about. While this course is mostly focused on theory the last chapter will also introduce you to some practical tools for Bayesian data analysis that you can start using today. Now, to be clear, in this course you won't learn how to crack secret Nazi messages, but you will learn the fundamental ideas behind Bayesian inference and how the framework of
13. Bayesian Data analysis: a tool to make sense of your data.
Bayesian data analysis can be used to make sense of your data.