3 Statistical decision theory

3.1 Formalism for statistical decision models

The payoff to a decision depends on the value of some unobserved parameter \(\theta\), which could be a vector. We have some system for generating a probability distribution \(\pi(\theta)\) over \(\theta\). In Bayesian approaches, the probability distribution \(\pi(\theta)\) used is the posterior distribution of \(\theta\) given the observed data: \(\pi(\theta | y)\). Other approaches exist for creating probability distributions over states