Full text: Actes du onzième Congrès International de Photogrammétrie (fascicule 6)

  
some of the acts the amount of this profit is unknown because it will be 
determined by some event which cannot be predicted with certainty. 
The choice among the acts may be made by assigning a definite nume- 
rical value to every consequence and by assigning a definite numerical 
weight to every event. 
Now we define the Conditional Value of a particular event: The value 
which the person responsible for a choice among acts attaches to the 
consequence Which that particular act will have if that particular event 
occurs. 
The Expected Monetary Value of our act is defined as: The weighted 
average af all the conditional values of the act — each conditional value 
being weighted by its probability. Decision theory concerns itself with 
choosing the best act (under uncertainity) wich is consistent with the 
basic psychological desires (expressed by a defined Decision Criterion) 
of the decision maker. 
The Decision Process. (The Two-possible-action-case.) 
It is assumed that it pays to test before the decision is made. One 
logical decision process comprises then the following nine points. 
l. Choose the decision criterion 
Due to the policy of our organisation we choose to use Bayes Decision 
Rule$): Definition: Compute the expected value of each act (i. e. mul- 
6) Other decision rules that might have been choosen are: 
A) The Maximax criterion: Choose the act wich maximises the maximum 
possible profit. 
B) The Minimax or Wald's criterion of pessimism: Choose the act with the 
minimum maximum loss. 
C) Hurwicz criterion of optimism: Apply a coefficient of optimism. If it is 
equal to one, we have A), otherwise we have a weighted combination of 
A) and B). 
D) The Savage criterion of regret: is the Minimax criterion app'ied — not to 
a payoff matrix — but to a risk or regret matrix, which shows the diffe 
rences between the payoff we receive and the one we could have received 
if the state of nature was known in advance. 
E) Laplace criterion of insufficient reason: Assume equally likley events. 
Add possible consequenses of each act and divide the number of possible 
events. Choose the act with highest result. (It is Bayes criterion without 
probability differences.) 
F) Maximum likelihood: Choose the best act for the state of nature which is 
most likley to occur. (This rule does only make use of little of the avail- 
able information.) 
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