Using the constructed quantities

As you might guess, once our constructs are defined we can use them just as though we had defined them from the keyboard. As an example, we will use them to emphasise some technical properties of the canonical directions and of the belief structure generated by the canonical directions. Our name for the particular belief structure is the belief grid. Let us see what happens when we adjust the belief grid by , instead of adjusting the belief structure by .

The following commands define a new collection, or base, to contain our belief grid, adjust the collection by the collection , and then display various results of the adjustment:

BD>base: Y = Y$

BD>keep: -cd

BD>adjust: [ Y / D ]

BD>show: v+, e*, a+

 
Figure 22:  Adjusting the canonical directions

giving the output shown in figure 22 (with further discussion in section 4.5). What should we notice about this sequence of commands and the output?

• we used our abbreviated syntax ``Y$'' to mean all those elements whose names start with the letter Y. At this point in time, [B/D] knows two such elements, and , so the base is defined to be the collection .
• we didn't want to retain the canonical directions for this adjustment, so we turned the option off. Otherwise our previous retentions would have been overwritten.
• we can combine output options for the SHOW:  command by supplying several options to the command, separated by commas.
• the results of the adjustment over the belief grid are just as we asserted above, as they constitute fundamental properties of the belief grid. Each canonical direction has an initial variance of unity by default, and the same resolution seen in figure 14. Each has an evaluated adjusted expectation identical to that seen earlier, in figure 17.
• the results for the belief structure are identical to those for the belief structure . This is to be expected as the two are equivalent in the sense that the quantities that generate also form a basis for .
• we also see the adjusted expectation formula for each canonical direction.