It is also worth mentioning that Bayesian classifiers, like Naive Bayes, are different from the type of Bayesian regression models described in this post. Naiv

It is also worth mentioning that Bayesian classifiers, like Naive Bayes, are different from the type of Bayesian regression models described in this post. Naive Bayes, for example, is more of a "machine learning" technique where the goal is to classify people into groups based on features. Naive Bayes is called Naive because it assumes that all regressors (x_j) are independent given the target variable (let's call it y and assume it is binary). In other words, the conditional log odds of y=1 given the x_j variables is equal to the sum of the log density ratios, where the log density ratio for variable x_j is ln(f(x_j|y=1)/f(x_j|y=0)). On the other hand, in the price elasticity example described in post we want to infuse outside knowledge into the model because we don't believe what it says on its own. This is a situation where interpretation and believability is an important part of the objective function because we will be running future pricing scenarios from the model. If you are building, say, a churn model to predict who is going to cancel their accounts, you probably wouldn't infuse your model with outside knowledge since cross validation accuracy is your main goal. You might regularize your model, however, which can be done in a number of ways (Bayesian or non-Bayesian). But in a pricing model or media mix model, and many other cases, the use case above is very real. I suggest reading the “Elements of Statistical Learning” by Hastie, Tibshirani, et al.