Bayes Theorem Examples: A Visual Guide For Beginners

by Scott Hartshorn

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.

Genres: Science, Nonfiction, Technology

90 pages, Kindle Edition

First published January 22, 2016

Reviews

[Sundar · Rating 4 out of 5]

After being impressed with the author's other guide on Probability (my review), I bought this ebook too with high hopes. It seemed to follow a different approach here, directly starting with the equation instead of intuition. I was losing hope when the author followed it up with the intuition for the components.

Bayes Theorem can be counter-intuitive for most people and the author has done a good job of driving the intuition as well as solve problems in this space. In order to make the learning durable, it's best to start applying as soon as one completes the book.

[Roberto Rigolin F Lopes · Rating 3 out of 5]

Practical, simple and straight to the point introduction to Bayes theorem. You can even download all the examples to play with numbers. Our intuition fails miserably when several occurrences of the same event happens; quite useful theorem.

[Brent · Rating 4 out of 5]

Good Succinct Review

This book gives a very good and quite succinct review of Bayes' Theorem with useful and easily understood examples laid out in tables and graphs showing both inputs and outputs. Several examples are shown using Excel (which are easily translatable to other spreadsheet programs). Useful for anyone who has heard of Bayes' Theorem but isn't quite sure what it is or whether it might be useful to them.

[Rodrigo · Rating 5 out of 5]

Scott’s book offers a fantastic introduction to Bayes’ Theorem. It simplifies complex ideas so effectively that even children can grasp them. Scott’s engaging writing style and the relatable examples he uses make the book a captivating read, especially for statistics enthusiasts. You’ll likely breeze through it in no time!

[Robert · Rating 3 out of 5]

Good introduction

Solid introduction. Likely requires a couple readings or an accompaniment; or, reader could follow offline and do the exercises. Overall: good.

[Darko Doko · Rating 5 out of 5]

Easy examples but have to it alone..or read some more

[Dwayne Roberts · Rating 3 out of 5]

Pretty good. The book would be improved with some editing. Misspelled words and missing punctuation distract. Also I expected a discussion of the Monte Hall problem, and was surprised at its absence.

[Kenneth E Mayer · Rating 5 out of 5]

Great summary of Bayes Theorem

This was a pretty good summary of Bayes. It took me about 90 minutes to go through the book. The excel sheets from the web are helpful.

[Bálint · Rating 2 out of 5]

First example is absolutely fantastic, then it speeds up and I lost track, so I can't comment on those. More typos than expected, but not that big deal.

[Vyacheslav Ilnytskyy · Rating 1 out of 5]

Awful. Standard examples from the internet, where authors explanation and interpretation is vague and confusing

[Mark Schulz · Rating 5 out of 5]

Bayes for beginners

A clear introduction to applications of Bayes theorem with recommended readings for those who want to dive deeper. Think Bayes is now a great read to follow this.