I will be making one observation at a time from one of many correlated distributions and each observation will fall into one of four categories.
If $p_i$$_j$ is the prior belief about the probability that i is observed from distribution j, what are posterior probabilities if i* is observed from distribution j*? Also, I am unsure what my covariance matrix would look like or how I would update it.
The only paper I have found that seems to be related is http://sankhya.isical.ac.in/search/63b3/8436fnl.pdf, but I had trouble following the notation.
Three prices are chosen: price of good 1, price of good 2, price of buying both. Each customer makes a decision (1, 2, both, or neither) and then a manager needs to update beliefs about the probability of each choice. I'll make the price choices discrete and make the prior correlation dependent on the distance between price vectors.
I think I already have a good idea of how I would like to simulate customer arrivals and the decision process.