The Bayesian Approach to Statistical Decision An Exposition

ly by the symbols a,, a2, a3. The one-to-one correspondence between action and state of world does, however, constitute a kind of ideal case; the loss function resulting from the inadmissibility of certain actions (fewer actions than states of the world) can easily be derived by introducing the opportunitycost idea. The crucial thing to remember is that, for each state of the world, the best admissible action is assigned zero loss and serves as the standard of comparison for the other actions. In short, the loss table is filled in vertically, not horizontally-measuring from the best action for each state of the world, not the best state of the world for each action. Comparing Tables 4 and 5, we see that the three remaining actions each have less expected loss than before; roughly speaking, by limiting the range of admissible actions we have reduced the possible loss owing to inappropriate action, inappropriateness being measured by loss in comparison with the best action remain-