BO 
p 1d.) 
  
  
  
Figure 1. General appearance of p(zid;) and p(z|d2) 
from which follows directly: 
ak 
P,(e|da) 2 Pr(iwk! « ak) < ] pk(zidi)dz = 1 — Pa (eld1)- 
0 
It is to be assumed that the p,(z|di)'s are often invariant for all the observations and always 
invariant for groups of the observations. 
The Baysian method proposed above is based on the principle of minimizing the classification error 
in terms of probabilities. A more elaborate approach could be taken by using a minimum risk 
principle where the costs of decisions are also considered (see e.g. Fukunaga, 1972). 
Application of evidence combination 
If the P,(da)'s (the a priori probabilities of the existence of a blunder) are set to be equal for all 
the observations, there is no operational difference compared to the method where risk level a is 
selected a priori. Both of the methods reject an abservation with a |wy| above a critical value 
which is a fixed constant for a group of similar observations. Instead of fixing the risk level, the 
probability of the existence of blunders is fixed. It would be natural to derive this probability on 
the basis of earlier, similar adjustment projects. 
More distinct differences are encountered when the P(dz)’s are determided individually for each 
observation. They can be interpreted as measures of the quality of the observations. If observations 
are produced mathematically, for example as a result of image target matching, this measure would 
be a number indicating the probability that a predifined accuracy has been achieved in the matching. 
In this case - as in general - it is essential that the probability is derived in such a way that it and 
the residual (in the adjustment model now under consideration) will be independent. 
Table 1 
Example of mapping linguistic 
statements or numeric grades to 
subjective probability numbers 
  
  
Linguistic statement | Grade | P(di) 
ultra excellent 6 1 
excellent 5 0:9999 
very good 4 0.999 
good 3 0.99 
very satisfactory 2 0.95 
satisfactory 1 0.90 
rejected 0 0 
  
  
  
  
  
If observations are done by a human, P(d2) is a subjective measure. Table 1 gives an example of how 
the operator’s judgement about the quality of an observation can be used as a basis for assigning the 
probability numbers for each individual observation. In a more fuzzy way, they can be interpreted 
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