Beta-Binomial
The Beta-Binomial prior is another example and a well-known model where we set a prior distribution on the parameter of the distribution of interest. Here we are going to use a binomial distribution with a θ parameter. The θ parameter can be seen as a probability that an event will occur or not, or a proportion of the positive events in a sequence of experiments. Therefore, the parameter θ takes values in [0,1].
Let's first review the Binomial distribution with a simple example: let's say we have a coin and we want to know if the coin is impartial or not when we play the heads or tails game. The game is to toss the coin N times and try to estimate what is the probability θ of obtaining a head. This problem is very important because it is the basis of many other models. You can replace the game of heads or tails with the result of experimentation (positive or negative), the result of a poll (yes or no), or any other binary answer.
Historically...
