Ewens sampling formula

Okay kiddo, let me tell you about Ewens sampling formula. Imagine you and your friends are playing with different colored marbles. You have a bag with lots of marbles of the same color, but each one has a different pattern on it. Your friends want to know how many different patterns there are in the bag.

Now, let's imagine that this bag has a LOT of marbles. So many that it's impossible to count every single marble and pattern. But you still want to know how many different patterns are in there. This is where Ewens' formula comes in.

The formula helps us estimate the number of different patterns in a big group of things (like marbles) based on how many of each type we've seen so far. It's like making an educated guess based on the patterns we have already seen.

To use the formula, we need to know how many marbles there are in total, how many different patterns we've already seen, and how many marbles we have of each seen pattern. The formula takes all of these things into account to give us an estimate of how many more unseen patterns there could be in the bag.

So now you know about Ewens sampling formula - a way to estimate the number of different patterns in a big group of things based on what we've already seen. Isn't that neat, kiddo?