Principle of maximum entropy

Imagine that you have a very big jar with lots of marbles of different colors in it. You know that there are red, blue, green, and yellow marbles inside, but you don't know how many of each color there are. Someone has mixed them all up, so you can't see them anymore.

Now, you want to guess how many marbles of each color there are. But you have no idea! So, what do you do? You use the principle of maximum entropy.

The principle of maximum entropy is a rule that says, when you don't know something, the best guess you can make is the one that is the most uncertain or least biased. It's like saying "I don't know, but maybe it's this..."

So, you start by assuming that every color of marble is equally likely. That means there's an equal chance of there being one red marble or one blue marble, or ten of each color. That's the most uncertain or least-biased guess you can make.

But then, you look closer. You notice that the jar looks more like it has mostly red marbles. You also think that having a few yellow or blue marbles would be normal, but having a lot of green marbles would be unusual. So, you adjust your guess based on what seems most likely.

The principle of maximum entropy tells us that, if we don't have any other information, assuming all possibilities are equally likely is the best guess we can make. But, if we do have some information, we can adjust our guess to be more likely based on what we know.

So, in the end, using the principle of maximum entropy helps us make the best guess we can when we don't have all the answers.