# The Azimuth Project Bayesian statistical decision theory (Rev #3)

## The idea

Bayesian statistical decision theory is a formal approach to making decisions under uncertainty. The big picture looks like this.

The model is at the heart of the framework. Typically it is based on a scientific theory concerning some aspect of the real world. It is a stochastic model with some adjustable parameters which can be used to calculate the probability of observing particular outcomes.

The prior is a probability distribution which represents what assumed about the value of the parameters before the data is seen.

The utility function, or loss function evaluates the consequences of taking possible actions, given parameter values. The difference between utility and loss is just a sign change. Business people usually talk about utility, since they are interested in maximizing profit; scientists usually talk about loss, since they are interested in minimizing errors.

The model, prior, and utility function encapsulate the assumptions that you must make in order to use this approach. The prior and utility are explicitly subjective: different people may legitimately make different assumptions here. The model is generally taken as less subjective, though this depends on context. Once you have made your assumptions, and obtained the data, the rest is automatic. It is just a calculation (though it may be a very complicated one) which will tell you what to do.