New facts should affect what we think, but how much they do so depends on what we already think.
Imagine being asked, "How certain are you that it'll rain later?" You look up. Dark Clouds. But should your answer depend on whether you're in Las Vegas or London, despite the same clouds hovering above you?
The surprising answer is yes. And knowing that it should is a decision-making superpower.
Bayesian Thinking is a tool that helps you make better decisions. It allows you to incorporate both your prior knowledge and new evidence into your decision-making process. Instead of just looking at new evidence in isolation, you update your beliefs based on where you started from.
Coming back to our example; it's obvious that it rains more in London than in Las Vegas. This is your prior knowledge. The dark clouds you now observe are new evidence of incoming rainfall — new evidence. Instead of making a guess about rainfall in isolation, you should update your beliefs depending on where you are observing those clouds.
Let's say you estimate that the probability of rain on any given day is 4% in Las Vegas and 38% in London. Now you observe dark clouds in both places. Your estimation should go up from 4% and 38%, respectively, but not to the same number. So your answer to the initial question of "how certain are you that it'll rain later" could be something like 47% for Las Vegas and 93% for London.
The mathematical foundation of Bayesian Thinking is Bayes' Theorem. But you don't need to understand the math to appreciate its impact on our thought process: new evidence updates our prior knowledge, but doesn't replace it. Whatever we believed before we observed something should influence what we believe after it.
Bayesian Thinking is being used in science, business, and politics to navigate uncertainty and make predictions. But a basic understanding of it can also be helpful for decision-making in your personal life. Without Bayesian Thinking, reasoning errors and false assumptions about the world and future events can be made.
“Under Bayes' theorem, no theory is perfect. Rather, it is a work in progress, always subject to further refinement and testing.”
— Nate Silver
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