Marginal likelihood

Imagine you have a puzzle box full of puzzle pieces. But you don't know what the picture on the puzzle is. You want to find out what the picture is, so you start putting the puzzle pieces together.

But as you put more and more pieces together, you realize that some pieces don't fit very well, and they don't really help you understand what the picture looks like.

That's kind of like how scientists use marginal likelihood. They have a bunch of data, like puzzle pieces, that they want to use to understand a bigger picture. But not all of the data is equally helpful.

Marginal likelihood helps scientists figure out which data is most important for understanding the bigger picture. It's like taking out the puzzle pieces that don't fit well, so you can focus on the ones that are really helping you see what the puzzle looks like.

Basically, marginal likelihood is a way for scientists to figure out which pieces of data are most important for understanding a bigger picture, so they can use their time and resources more efficiently.