Adjusted variances

We display the adjusted variances by using the v  option of the SHOW:  command:

BD>show: v

 
Figure 12:  Adjusted variances

giving the output shown in figure 12. This shows the adjusted variance (informally the remaining uncertainty) for each quantity of interest: and .

If we change our option from v  to v+  we see further details on the adjusted variances:

BD>show: v+

 
Figure 13:  Adjusted variance details

giving the output shown in figure 13. The results for both the simple and the detailed output are discussed in section 4.2. Technically, for individual quantities this output consists of the following information: reading from left to right (and using the output for to illustrate) we have

• the name of the element, ;
• the element's initial variance, ;
• the element's adjusted variance, ;
• the element's resolved variance, ;
• the element's current resolution, .

The last row of the output (interpreted in section 4.3) contains results about the effect of adjustment on uncertainties within the entire belief structure taken as a whole. Reading from left to right, we have

• the name of the belief structure of interest, ;
• we summarise the prior uncertainty in the belief structure as the rank of the variance matrix specified over , this rank being equal to the number of canonical directions for the belief structure. The notation we use for this summary of the uncertainty in the belief structure is .
• we summarise the adjustment uncertainty of the belief structure by the sum of the adjustment variances for the canonical directions. Our notation for this quantity is .
• we summarise the resolved uncertainty of the belief structure as the sum of the resolved variances for the canonical directions. Our notation for this is .
• Analagously with the individual elements, the resolution for the belief structure is the resolved uncertainty divided by the prior uncertainty. We will use the same notation for belief structures as well as for individual elements, and so our notation for this quantity is .