Bayesian model comparison

Okay, so imagine you're trying to decide which toy you want to play with - your truck or your doll. You could just randomly pick one, or you could think about which one you like better based on some clues.

Bayesian model comparison is kind of like trying to pick the toy you like better, but instead of toys it's math models. Math models are like different sets of rules that help us predict or explain things.

Let's say we have two math models that could help us understand how plants grow better: Model A and Model B. We want to figure out which model is better, but we can't just randomly pick one. We need to gather some clues to help us decide.

So we start by gathering some data about plant growth, like how much sunlight the plants get and how much water they get. Then we compare how well each math model predicts the plant growth based on those clues.

Model A might predict that plants grow taller with more water and more sunlight. Model B might predict that plants grow taller with less water and less sunlight. We can see which model is better by looking at how well it fits the actual data we collected on plant growth.

If we find that Model A predicts plant growth better than Model B, we can say that Model A is the winner! That means we have a better idea of how plants grow based on the clues we gathered and the math model we used to make sense of it.

So basically, Bayesian model comparison is a way to help us figure out which math model is better at explaining or predicting things, based on the data we have available.