When we learned the principles of Bayesian inference in Chapter 3, Introducing Bayesian Inference, we saw that as the amount of training data increases, contribution to the parameter estimation from data overweighs that from the prior distribution. Also, the uncertainty in parameter estimation decreases. Therefore, you may wonder why one needs Bayesian modeling in large-scale data analysis. To answer this question, let us look at one such problem, which is building recommendation systems for e-commerce products.

In a typical e-commerce store, there will be millions of users and tens of thousands of products. However, each user would have purchased only a small fraction (less than 10%) of all the products found in the store in their lifetime. Let us say the e-commerce store is collecting users' feedback for each product sold as a rating on a scale of 1 to 5. Then, the store can create a user-product rating matrix to capture the ratings of all...