
Elements of decision theory 47
L(θ, δ)
θ δ
ǫ
L(θ, δ)
θ δ
(A) (B)
1
0
1
0
ˆ
θ
1
ˆ
θ
2
FIGURE 2.4 The one-dimensional loss function that leads to MAP estimators for
continuous (A) and discrete (B) cases.
the following two examples:
Example 2.6: Pulling goaltender in an ice hockey game
Suppose a hockey team A is down 1 goal losing to team B and there are 30
seconds left in a play off ga me (losing team is out of competition). Suppose we
consider only three outc ome s : (1) Team A sc ores keeping its changes alive and
forcing the overtime, (2) Team B scores winning the match by the difference
of two goals, and (3) there are no more goals and team B wins by one goal.
Therefore ...