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Bayesian Methods: From Theory to Real-World Applications
A Practical Guide to Using Bayesian Techniques in A/B Testing and Uplift Modeling
Introduction
The Bayesian approach is commonly applied in fields such as finance, marketing, and medicine. In this paper, I focus on how it can be used for A/B testing.
I begin with a simple example to explain Bayes’ Theorem and show how it helps handle uncertainty and make better decisions.
Next, I discuss how Bayesian testing differs from traditional methods like t-tests and why it can be more effective for analyzing A/B test results.
The main part of the paper explores Bayesian A/B testing in marketing, particularly with uplift models, comparing its performance to traditional approaches.
Finally, I share the results and business insights, highlighting how Bayesian methods support smarter decision-making in uncertain situations.
Bayes’ Theorem Made Simple
I will use a Tall Tale of Students and Sports Clubs to explain Bayesian theory.
If you’re familiar with Bayesian theory, jump to the next section.
Imagine this: I’m a student at a large school with hundreds of fellow students. There’s a popular sports club on campus that everyone is buzzing about, but only 5% of the students join. So, out of every 100 students, only about 5 are members of this club.
Here’s something interesting about the sports club members: there’s an 80% chance that any student in the club is tall — like, top 10% in height among all students. So if you meet a club member, chances are they’re towering over most people!
If someone asks, “What’s the chance that a randomly selected student who is among the tallest 10% in the school joined the sports club”?
At first glance, it might seem tricky, but this is where Bayes’ Theorem comes into play. Let’s break it down step by step using some simple math:
P(Club Member) = 5% or 0.05
Only 5% of the students are in the sports club.P(Tall | Club Member) = 80% or 0.80
If a student is in the club, there’s an…
