Hi,

I am new to Stan and have the following question.

I have n realizations of 8 Bernoulli random variables X_1,...,X_8. I want to estimate the pointwise mutual information, pmi_{ij} = \log\frac{P(X_i=1, \ X_j=1)}{P(X_i = 1)P(X_j=1)} for each pair, i.e. with i,j \in 1,...,8 and i \ne j. So I need to estimate the marginal and pairwise joint probabilities.

So far, I have two ideas:

- Create a matrix with 8 columns for the marginal responses, and a matrix with 28 columns for the joint responses (28 possible pairs). Then, estimate a the probability of response for each column using likelihood
`x ~ bernoulli(p)`

, with some prior on`p`

.

- Create a matrix with 256 columns, where each column is a indicator variable for one specific combination of X_1,...,X_8. The proceed as above, and sum the appropriate
`p`

’s to get the marginal and pairwise joint probabilities.

The first approach seems preferable (since I don’t care about the joint probability of more than 2 variables). Is there any reason to prefer the second approach? Or is there a better approach alltogether?

Thank you.