Table 2 
An example of evolution from basic 
statististic to the order statistics 
  
  
  
lal Case | 
RA BB C F5 
1 |1.0 |.999 |.999 1.999 | 
2 |1.0 |.9999 |.9999 |.999 | 
3 |1.0 |.9999 |.999 |.999 
+ [99 [99 7 1.99 1.996 
5 1.0 10  |.9999 |.999 | 
  
  
  
  
  
to be numbers that indicate the operators! believe that the observation is 'good'. The generally 
good quality of photogrammetric and geodetic observations has been taken into consideration in 
the assignment of these numbers. 
It is possible to fine-tune the system by adjusting the probability numbers because of the subjectivity 
of those numbers. This enables compensation for the inaccuracies of p(x|d2) as can be observed 
from the decision rule where only the products P, (d;) P.(e|d;) matter. 
In several papers dealing with blunder detection, it has been proposed that the statistical methods 
are only to be used to alarm the user about the likely presence of a blunder. They urge that the final 
decision has to be made by a human. This suggests that there really is a subjective component 
in blunder detection, and that the user of an adjustment program is supposed to prefer some 
observations over the others. The Baysian approach is cleary one way to explain the problematics 
involved. It also gives a rigorous starting point for further developments. 
Further questions on evidence combination 
The principles of evidence combination were studied above in a case in which the observation was 
specified a priori. Therefore, the T-distribution was applicable to Pk(z|di). In an algorithm for 
blunder detection this approach is not feasible but any observation has to be considered in the 
context of all the observations in the adjustment. 
When *conventional" blunder detection methods are considered, one of the reliable strategies is 
to reject one observtion at a time, starting from the one having the largest externally Studentized 
residual. These methods have been called sequential (Mikhail and Graig, 1982), (Grün, 1984) or 
iterated (Kok, 1984) data snooping techniques, being actually a special case of the more general 
search method introduced in (Sarjakoski, 1986). The maximum of the test values (or the first one 
in the decreasingly ordered sequence of test values) does not follow the T-distribution (under the 
typical null hypothesis) but an ordered version of it, called T,,,, *. Rigorous use of Tmaz Statistics 
is difficult in practice, due to its dependency on the variance-covariance matrix of residuals which 
is determined by the functional and stochastical model involved. 
When the Baysian-classification-based method is applied in a similar, sequential manner, extra 
complexities occur because of the-a priori probabilities, Pa (eild1), which may vary over the whole 
set of observations. In a sequential Baysian-classification-based method, it is reasonable to reject 
observations in increasing order of confidence ratios, cr, (compare with the likelihood ratio in 
Fukunaga, 1972): 
Pk (di le) . Pk(d1) 2 Pk (edi) 
Cre = = 
Pa(daje)  Pe(d2) Pa(eldz) 
  
The decision rule is then: 
crm = min(er,) 
Crm < 1 — 0bs.,, € da 
  
In (Sarjakoski, 1986) the term T,,4 was used instead. Tmaz is considered to be more descriptive, 
however, because the distribution applies only to the maximum element of a vector of elements. 
202