A visual introduction to Bayesianism
Summary
“To see is to believe”, that famous quote, is essential to delve into one of the most fascinating actual domains of Mathematics and Statistics, known as Bayesianism. The theory about it has been known since the 18th century, but it is only now that this rule of probability is gaining success among scientists as an alternative to machine learning. Even the finder of this rule did not find it “exciting” and just considered it another mathematical equation. But the truth is very balanced, as some rare scientists have been trying to understand that equation. Anyway, it is still uneasy for the newbie to follow up because of the complexity of this rule that even embraces the philosophy of life. Through this note, we build a comprehensive and unique visual way to give critical clues for the scholar to begin the long march through Bayesianism.
Contents
2 The Frequentist vs the Bayesian
3 Why is the Bayesian approach so powerful?
That formula is quite simple. Don’t let the wording confuse you. It says that if a certain proportion of items in a sample have property A, and another proportion has property B, we can figure out the proportion of items that have both properties. We do this by multiplying the percentage of items that have property A by the percentage of those that also have property B, and vice versa.
So, Pierre Simon Laplace, a famous French Scientist, later recognized the true significance of this equation. He realized that it could be used to calculate conditional probabilities, meaning the probability of event B given that event A has occurred. Before Laplace, it was only possible to calculate probabilities when the cause was known.
Today, Bayes’ rule has become increasingly important in scientific thought. However, many people, including some in the scientific community, struggle to understand how it works or what it represents.
1. The Marlon Case
We’ll start with a puzzle. Imagine that you’re walking across the campus of some large university and you meet a guy. Let’s call him Marlon. You chat with Marlon for a few minutes and you notice that Marlon is shy. Meaning he’s not making eye contact very often. He’s mumbling. And a question arises for you.
If you had to make a guess, do you think Marlon is more likely studying for a math Ph.D. or attending a business school?
4. Conclusion
Bayesianism is a powerful tool with many practical uses. It offers a fresh way to tackle common problems that the traditional Frequentist approach may struggle to solve. Instead of being rigid, it’s about adapting our beliefs based on new information, echoing Socrates’ famous quote “The only true wisdom is in knowing you know nothing.”
Do you think most scientists who adopt Bayesianism also have an interest in philosophy? It’s an interesting question for those who follow Bayesian principles. If you’d like to learn more about this topic, please visit the link below.
