What are bayesian methods?

Bayesian methods are like having a super-smart friend who guesses what you're thinking based on clues from before.

Imagine you have a bag full of marbles, some red, some blue. You can't see inside the bag, but every time you pull out a marble, you learn something new about the bag. At first, you might think there are equal numbers of red and blue marbles. But after pulling out several red ones in a row, your smart friend would say, "I bet there are more red marbles than blue ones!" That’s Bayesian thinking, using what you already know (prior knowledge) to make better guesses when new clues come in (new evidence).

Think of it like playing a game. You start with a guess (like saying half the marbles are red). Every time you pick one, you update your guess. If most of them are red, you adjust your guess to say there are probably more red marbles, and maybe even tell your friend how sure you are!

So Bayesian methods help us make smarter guesses by learning from each clue we get, just like your super-smart friend who gets better at guessing every time they play the marble game with you.