# Applying bayesian inference to a time based problem

I have a N*M matrix with N customers and M products. Each row of this matrix is a M dimensional vector like [1 3 4 1 5 ....] where each value represents how many times that customer has chosen this product in the past. Given this data, I want to predict this M dimensional vector for each customer in the future.

This prediction should be such that, for each customer, the M length vector should sum to 1(the vector should hold normalized probabilities for each product being clicked. For ex- [0.99 0 0 .. 0 0.01] for customer i, says that the product 1 has the highest probability of being chosen and product M has 0.01 probability of being chosen and others have 0 probability).

How do I apply bayesian inference to this problem? I can do MLE by dividing the counts in each vector by its total(for ex- for customer i, his product vector can be ([1 3 4 1 5 ....] / sum([1 3 4 1 5 ....]) and this will be normalized). I want to know how to apply bayesian inference to solve this problem?