Bayes’ Here, Bayes’ There, Bayes’ Theorem is Everywhere
To say that Bayes’ Theorem is important to statistics and analysis would be an unfair understatement. You learn it in almost every statistics class; you’ll see it in other forms of mathematics, economics, game theory, almost everywhere but the real world – or so you think.
While the theory’s formula itself seems too quantitative to apply in real life, a Bayesian way of thinking in life is far more common than we see. In class we learned that Bayes’ Theorem is a way to calculated a conditional probability. However, if we break down these mathematical terms, we see that a conditional probability is simply “B has already happened, so now what is the chance of A happening?” For example, I could ask myself – it’s my birthday today, what’s the chances of me getting a gift now? That question itself is not very statistical or quantitative in nature, but it follows the exact train of thought that Bayes’ Theorem follows.
The article discusses a “Bayesian approach to life,” in which we think intuitively: “We use prior knowledge from our experiences and memories, and new evidence from our senses, to assign probabilities to everyday things and manage our lives.” In class, we used Bayes’ theorem to predict information cascades and figure out what a particular person should choose based on their prior knowledge.
However, applying this “Bayesian approach” could mean that just intuitively, we could figure out how and where an information cascade could begin. When we look at it, Bayes’ Theorem is much more logical than we realize. We can also think about the “rich-get-richer” idea in terms of this intuition. In class and from the textbook, we understand this concept in relation to the power law, however it is just as applicable without all the math.
Let’s take some assumed prior knowledge: say I have 10 friends and my enemy has only 2 friends. Because I have 10 friends, who might say, each have 1 or 2 more friends, I am more likely to connect to those people as well. Meanwhile, my enemy only has 2 connections to expand upon. We see this “rich-get-richer” idea in real life all the time. Celebrities get more and more popular meanwhile to break into the industry is almost impossible.
Bayes’ Theorem is everywhere, and you’re almost always thinking about it whether you realize it or not. In class, we learned the formula, but the truth is that you have been using this theorem probably all throughout your life. And now maybe we’ll understand why it is so important to the world.