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Constructing the bearing

 

In section 12.1 we showed you how to retain the canonical directions as assignments and we went on to construct them as quantities. We can do the same with the bearing vector: it is, after all, a simple linear combination of elements in tex2html_wrap_inline8606 . To retain the bearing we need to tell [B/D] before making the adjustment, and this is achieved by issuing the command

BD>keep: b=Z tex2html_wrap_inline6116

This line informs [B/D] that the bearing for a subsequent adjustment is to be retained as an assignment named ``Z'' (here, too, we can choose another name if we wish). Suppose that we now effect the creation and retention of the bearing as an assignment by issuing another adjustment command:

BD>adjust: [B/D] tex2html_wrap_inline6116

Firstly we can verify that [B/D] has added the newly created assignment that represents the bearing to the others that we created earlier, and saw in figure 20:

BD>look: (a) tex2html_wrap_inline6116

  figure7283
Figure 23:  Assigning the bearing

giving the output shown in figure 23. The first assignment that we see corresponds to the bearing that we saw for the first time in section 11.3, and we see also the assignments tex2html_wrap_inline8956 and tex2html_wrap_inline8966 retained earlier. Now, just as we did for the canonical directions, we will go on to build the bearing and then assess it as a quantity by displaying its variance and covariances with tex2html_wrap_inline8580 and tex2html_wrap_inline8582 :

BD>build: Z tex2html_wrap_inline6116

BD>look: (v1) B, Z tex2html_wrap_inline6116

  figure7299
Figure 24:  Constructing the bearing

giving the output shown in figure 24. This shows that we have indeed constructed tex2html_wrap_inline9937 , and have displayed the variance matrix (with a variance for tex2html_wrap_inline9937 and covariances between tex2html_wrap_inline9937 and tex2html_wrap_inline8606 deduced by [B/D] from the linear combination supplied) for tex2html_wrap_inline8580 , tex2html_wrap_inline8582 and tex2html_wrap_inline9937 . Notice how we modify the LOOK:  command to restrict the output to the detail that we want: we add a list of bases and elements to the commandgif.

We can use this output to examine the covariances between the bearing and the elements of tex2html_wrap_inline8606 , and verify that these covariances represent the changes in expectation for each quantity due to the adjustment. We can also verify another property, namely that the size of the adjustment shown in figure 18 is equal to the prior variance of the linear combination representing the bearing.


next up previous
Next: Adjusting beliefs in stages Up: Further [B/D] techniques Previous: Using the constructed quantities

David Wooff
Thu Oct 15 12:20:04 BST 1998