Building assignments

We have retained our canonical directions as assignments; as linear combinations. The point is that by retaining them in this way (and not as elements), we don't have to take up room by defining the covariance matrices that would associate them with the other quantities which are, as elements, automatically associated with specific variance-covariance matrices. Hence the assignment is a very efficient way of retaining some quantities.

However, sooner or later we may want to construct elements from the assignments that exist, and we do so using the BUILD:  command. This command can be used in different ways, for different purposes. To construct our canonical directions, which exist as assignments Y1 and Y2, we use it as follows:

BD>build:Y1

BD>build:Y2

Now we will use some of the commands that we used earlier in section 8 to examine our construction. Issue the following command to inspect the names of elements and their associated covariance matrix:

BD>look:(e,v1)

 
Figure 21:  Constructing the canonical directions

giving the output shown in figure 21. There are several observations to be made about this sequence of commands and their resultant output:

• we combined the commands LOOK: (e) (for looking at elements) and LOOK: (v1) (for looking at beliefs) into the single command LOOK: (e,v1), which gave us both. If we like, we can always combine the arguments of the LOOK:  command in this way: we use a comma to separate alternative arguments to the command.
• and are now known to [B/D] as elements called Y1 and Y2 respectively, and [B/D] has determined from their definition as linear combinations of pre-existent elements that each has expectation zero.
• we see the full covariance matrix specified over all six elements. [B/D] automatically deduced the necessary covariances over and , and between them and the pre-existent elements, from the linear combinations supplied.
• we asserted above that a property of the canonical directions is that they are uncorrelated and have unit variances. These features are readily verifiable here.