03-decision-01-decisions.Rmd

## Bayesian Decision Making

To a Bayesian, the posterior distribution is the basis of any inference, since it integrates both his/her prior opinions and knowledge and the new information provided by the data. It also contains everything she believes about the distribution of the unknown parameter of interest. 

However, the posterior distribution on its own is not always sufficient. Sometimes the inference we want to express is a **credible interval**, because it indicates a range of likely values for the parameter. That would be helpful if you wanted to say that you are **95% certain** the probability of an RU-486 pregnancy lies between some number $L$ and some number $U$. And on other occasions, one needs to make a single number guess about the value of the parameter. For example, you might want to declare the average payoff for an insurance claim or tell a patient how much longer he/she has to live. 

Therefore, the Bayesian perspective leads directly to **decision theory**. And in decision theory, one seeks to minimize one's expected loss.