Bayes Theorem Examples: A Beginners Visual Approach to Bayesian Data Analysis

If you are looking for a short beginners guide packed with visual examples, this booklet is for you.

From Google search results to Netflix recommendations and investment strategies, Bayes Theorem (also often called Bayes Rule or Bayes Formula) is used across countless industries to help calculate and assess probability.

Bayesian statistics is taught in most first-year statistics classes across the nation, but there is one major problem that many students (and others who are interested in the theorem) face. The theorem is not intuitive for most people, and understanding how it works can be a challenge, especially because it is often taught without visual aids.

In this guide, we unpack the various components of the theorem and provide a basic overview of how it works - and with illustrations to help. Three scenarios - the flu, breathalyzer tests, and peacekeeping - are used throughout the booklet to teach how problems involving Bayes Theorem can be approached and solved.

Over 60 hand-drawn visuals are included throughout to help you work through each problem as you learn by example. The illustrations are simple, hand-drawn, and in black and white.

For those interested, we have also included sections typically not found in other beginner guides to Bayes Rule. These include:

• A short tutorial on how to understand problem scenarios and find P(B), P(A), and P(B|A). For many people, knowing how to approach scenarios and break them apart can be daunting. In this booklet, we provide a quick step-by-step reference on how to confidently understand scenarios.


• A few examples of how to think like a Bayesian in everyday life. Bayes Rule might seem somewhat abstract, but it can be applied to many areas of life and help you make better decisions. It is a great tool that can help you with critical thinking, problem-solving, and dealing with the gray areas of life.



• A concise history of Bayes Rule. Bayes Theorem has a fascinating 200+ year history, and we have summed it up for you in this booklet. From its discovery in the 1700’s to its being used to break the German’s Enigma Code during World War 2, its tale is quite phenomenal.



• Fascinating real-life stories on how Bayes formula is used in everyday life.From search and rescue to spam filtering and driverless cars, Bayes is used in many areas of modern day life. We have summed up 3 examples for you and provided an example of how Bayes could be used.



• An expanded definitions, notations, and proof sectionWe have included an expanded definitions and notations sections at the end of the booklet. In this section we define core terms more concretely, and also cover additional terms you might be confused about.



• A recommended readings sectionFrom The Theory That Would Not Die to a few other books, there are a number of recommendations we have for further reading. Take a look!

If you are a visual learner and like to learn by example, this intuitive booklet might be a good fit for you. Bayesian statistics is an incredibly fascinating topic and likely touches your life every single day. It is a very important tool that is used in data analysis throughout a wide-range of industries - so take an easy dive into the theorem for yourself with a visual approach!