Bayesian modeling

The posterior encapsulates the philosophy of Bayesian modeling and changes how we view the model represented by . In Bayesian modeling, there is not a single “correct” underlying value of , for which we construct uncertain estimates. Instead, different values of have different probabilities given the available data or evidence. is a random variable, and we update what we think is the distribution of that random variable using Bayes’ theorem and the additional data or information we receive.

With that statement about the philosophical interpretation of the posterior made, we now move on to how we use the posterior in a calculational sense. There are two potential ways in which we can use the posterior distribution:

• To evaluate expectation values. Here, we are using the posterior as it is intended, as a distribution. Here, the posterior is used to calculate predictions over lots of different models. This is called Bayesian model averaging...