Bayesian inference using Gibbs sampling
Think of Bayes theorem as a recipe that helps us figure out how likely something is to be true. But sometimes the recipe can be a little complicated and we need to use another recipe to help us. That's where Gibbs sampling comes in.
Imagine you are trying to figure out how likely it is to rain tomorrow based on what you know about the weather today. We can use Bayes theorem to help us figure this out. We already have some information about the likelihood of it raining and also some information about how likely it is to rain depending on certain factors like if it's cloudy or sunny.
Now, let's say we have other factors that we don't know yet like the temperature, humidity, and wind speed. These factors can also affect whether it's likely to rain or not. But we don't know how much influence they have. Using Bayes theorem, we can try to figure out these unknown factors by guessing them and then seeing how likely it is to rain given those guesses.
This is where Gibbs sampling comes in. It's like a helper recipe that tells us how to take guesses for these unknown factors. We do this by taking one guess at a time for each of the unknown factors and seeing how likely it is to rain given that guess. We keep doing this over and over until we get a good idea of what these unknown factors could be.
So, in summary, Bayes theorem is a recipe to figure out how likely something is to be true based on other information. Gibbs sampling is like a helper recipe that helps us take guesses for unknown factors when using Bayes theorem.
Imagine you are trying to figure out how likely it is to rain tomorrow based on what you know about the weather today. We can use Bayes theorem to help us figure this out. We already have some information about the likelihood of it raining and also some information about how likely it is to rain depending on certain factors like if it's cloudy or sunny.
Now, let's say we have other factors that we don't know yet like the temperature, humidity, and wind speed. These factors can also affect whether it's likely to rain or not. But we don't know how much influence they have. Using Bayes theorem, we can try to figure out these unknown factors by guessing them and then seeing how likely it is to rain given those guesses.
This is where Gibbs sampling comes in. It's like a helper recipe that tells us how to take guesses for these unknown factors. We do this by taking one guess at a time for each of the unknown factors and seeing how likely it is to rain given that guess. We keep doing this over and over until we get a good idea of what these unknown factors could be.
So, in summary, Bayes theorem is a recipe to figure out how likely something is to be true based on other information. Gibbs sampling is like a helper recipe that helps us take guesses for unknown factors when using Bayes theorem.