Statistical Decision Theory is best understood in the context of dynamic planning under uncertainty. In such a context, decisions in the present must be made based on a limited amount of information. The decisions in the present have an immediate impact as well as a dynamic impact in that they may influence the amount of future information and the kinds of future choices available.
The language of probability is natural for characterizing uncertainty, and beliefs in the presence of additional information are naturally updated using Bayes' rule. Expected utility provides a clearcut description of preferences and allows for a straightforward formulation of the decision problem.
Solving decision problems in the presence of uncertainty often require the use of sophisticated Monte Carlo Simulation and Optimization techniques.
For an illustration of a dynamic decision problem in the presence of uncertainty, click here.
George Dantzig - Inventor of Linear Progamming
My Research
Likelihood Subgradient Paper