Bayesian hierarchical modeling
Bayesian hierarchical modeling is like playing with building blocks.
Do you remember playing with building blocks? You start with a big block and then add smaller blocks on top of it to make a tower. But sometimes you might want to make two towers that are similar but a little bit different. Maybe one tower is taller, or maybe one tower has more blue blocks than the other.
Bayesian hierarchical modeling is like building towers with building blocks, but instead of just making one or two towers, we can make lots and lots of towers, all with slightly different colors and shapes.
How do we do that? Well, we start with some basic building blocks, which we can call "prior knowledge." This is what we already know about the world before we start making our towers. Let's say we know that towers usually have a square base, and they get narrower as they go up. That's our prior knowledge.
Then, we take those basic building blocks and put them together to make a tower. But instead of just making one tower, we make lots and lots of towers, with different colors and shapes. Each tower represents a hypothetical situation that we might encounter in the real world.
For example, we might make a tower that represents a group of people who are all about the same height, or we might make a tower that represents a group of people who are all different heights. Each of these towers is a different hypothesis about what we might see in the real world.
But we're not done yet! We also want to make sure that our towers are consistent with each other. We want to make sure that the towers with more blue blocks also tend to be taller, and the towers with more red blocks tend to be shorter.
So, we put all of our towers together into a big pile, and we look for patterns. We might notice that the towers with more blue blocks tend to be taller, or we might notice that the towers with more red blocks tend to be shorter. These patterns help us understand how our prior knowledge (the basic building blocks) can be combined with new information (the towers) to make better predictions about the world around us.
And that's what Bayesian hierarchical modeling is all about! It's like playing with building blocks, but instead of making towers, we're making predictions about the real world based on what we already know.
Do you remember playing with building blocks? You start with a big block and then add smaller blocks on top of it to make a tower. But sometimes you might want to make two towers that are similar but a little bit different. Maybe one tower is taller, or maybe one tower has more blue blocks than the other.
Bayesian hierarchical modeling is like building towers with building blocks, but instead of just making one or two towers, we can make lots and lots of towers, all with slightly different colors and shapes.
How do we do that? Well, we start with some basic building blocks, which we can call "prior knowledge." This is what we already know about the world before we start making our towers. Let's say we know that towers usually have a square base, and they get narrower as they go up. That's our prior knowledge.
Then, we take those basic building blocks and put them together to make a tower. But instead of just making one tower, we make lots and lots of towers, with different colors and shapes. Each tower represents a hypothetical situation that we might encounter in the real world.
For example, we might make a tower that represents a group of people who are all about the same height, or we might make a tower that represents a group of people who are all different heights. Each of these towers is a different hypothesis about what we might see in the real world.
But we're not done yet! We also want to make sure that our towers are consistent with each other. We want to make sure that the towers with more blue blocks also tend to be taller, and the towers with more red blocks tend to be shorter.
So, we put all of our towers together into a big pile, and we look for patterns. We might notice that the towers with more blue blocks tend to be taller, or we might notice that the towers with more red blocks tend to be shorter. These patterns help us understand how our prior knowledge (the basic building blocks) can be combined with new information (the towers) to make better predictions about the world around us.
And that's what Bayesian hierarchical modeling is all about! It's like playing with building blocks, but instead of making towers, we're making predictions about the real world based on what we already know.