Bayes Theorem Examples

If you are looking for a short guide full of interactive examples on Bayes Theorem, then this book is for you

From spam filters, to Netflix recommendations, to drug testing, Bayes Theorem (also known as Bayes Theory, Bayes Rule or Bayes Formula) is used through a huge number of industries.  The reason it is so useful is it provides a systematic way to update estimated probability as new data is found out.

Bayesian data analysis is taught in many introduction to statistics classes, however the problem is that it is not taught in a very intuitive way.  This book, instead of focusing on the probability theory, focuses on building a deep understanding of how bayesian statistics work.  This book contains a number of visual examples to build that understanding.  Additionally every example in this book has been solved using Excel, and the Bayesian Excel file is available for free download to allow you to easily work the examples along with the book.

This book uses a building block approach to help the reader understand how Bayes Theorem works in real like, in addition to the probability theory.   The topics covered are

• Bayes Theorem Basic Example - A first example to show how Bayesian data analysis works when you have a single new piece of data to update initial probabilities
  

• Updating Probabilities With Multiple Pieces Of New Data - What if instead of a single piece of data you have a lot of new measurements to update your probabilities
  

• Bayes Theorem Terminology - The formal names for the different parts of the bayes theorem equation, and how does relate to a more everyday understanding
  

• Are You A Winning Tennis Player? - Use the results from tennis matches to determine what your likely long term win rate is
  

• Dealing With Errors In Your Data - In real life you are unlikely to have the pure error free data that you see in most examples.  But if you actually want to use bayesian data analysis to solve real life problems, you need to account for the fact that some measurements will be wrong, or the data will be entered incorrectly, or there will be other errors.  This section shows how to deal with those errors and still get accurate probability estimates.
  

• Historical Successes of Bayes Theorem - One of the most famous successes of bayesian data analysis is the German Tank Problem.  This was the problem of estimating how many tanks and other pieces of high value equipment the enemy force had, using only a few pieces of captured equipment.  Bayesian statistics solved this problem better than espionage, and this example shows how it was done
  

• Classic Uses Of Bayes Theorem Today - A current famous application of bayesian statistics is the drug testing problem.  This problem asks how likely a person who got a positive result, for instance on a drug test or a test for disease, is to actually have that disease or be a user of the drug, vs. having  a false positive on the test
  

If you are a person that learns by example, this booklet might be a good fit for you.  It is a very important topic in a wide range of industries - so dive in to get an intuitive understanding!