Consider a standard Bayes linear influence diagram for the adjustment of
B by D, and then partially by F, and suppose also that
observations d and f become available.
The adjustment by D results in a portion of the B node's outer
sector being shaded to show the proportion of uncertainty across the
collection B, 
, resolved by
adjusting by D. Additionally, the corresponding inner sector is shaded
according to the magnitude and direction (too big/too small)
of the size ratio for the adjustment, 
. Both shadings (outer
and inner) reflect summaries across the collection B assessed for D
globally. A further partial adjustment by F induces similar shadings
for the partial adjustment, so that an extra portion of B's outer node
is shaded to reflect the extra variance resolution 
from
fitting on F in addition to D, and the corresponding inner node
shading depicts the partial size ratio 
.
The idea behind the canonical wheel influence diagrams is to partition
the global summaries , ,
according to the canonical quantities generated by the
two adjustments. This follows naturally as follows. Suppose that the
adjustment of B has r
canonical quantities 
with resolutions 
. Then the global proportion of variance
resolved,
is naturally partitioned into 
, where 
is
by convention the amount of prior uncertainty in the collection B.
Therefore, the nodal area represented
by 
can be partitioned into what we term r spokes,
each of which is a sector corresponding to a canonical quantity 
,
with outer node shading 
.
If there are observations then we also shade part of each inner spoke to
show diagnostics. The diagnostics shown are essentially the values of
the size ratios for the canonical quantities, and are thus more-or-less
comparable with the diagnostic shadings shown for standard influence
diagrams. A slightly different scaling strategy has been chosen,
however, as follows.
The proportion of area shaded depends on the value of
the corresponding size ratio, 
, divided by a threshhold
set by the spokeshade control, which is at 8.0 by default.
Proportions larger than unity are clipped at unity. Therefore by
default, size ratios of 4.0, 8.0, and 12.0 will result in 50%, 100%,
and 100% inner sector shadings. Threshholds should be chosen so that a
very surprising size ratio (``surprisingness'' can vary from context to
context) results in about full diagnostic shading, so that the degree of
shading conveys the degree of alarm. Bear in mind that the prior
expectation of every size ratio is unity.
The colour of the shading can be
altered using the spokecolour control.
The partial adjustment similarly results in a collection of partial canonical quantities which form a natural partition for the global summaries for the partial adjustment. Thus, we partition the sector previously corresponding to the partial resolved uncertainty into separate spokes, depending upon the number of partial canonical quantities, i.e. the rank of the partial resolution matrix. Size ratio diagnostics are shaded accordingly and similarly.
Sometimes the number of canonical quantities for an adjustment can be so large that too many spokes would be drawn on the canonical wheel, so offering little value as a means of understanding an adjustment. In such cases you can reduce the number of spokes that are drawn by using the spokes control. If you wish to see shadings for the first q<r canonical directions only, use the spokes control to limit the number of spokes drawn to q canonical quantities. This will then produce node shadings for q+1 spokes, with the extra shading in the final spoke aggregating the resolved uncertainty and diagnostic information for the last q-r canonical directions. The amount of outer and inner shading drawn for the aggregated spokes will sum to the same amount of shading that would have been observed had all the spokes been drawn.
Note that the spokes are drawn anticlockwise in order of magnitude of the canonical resolutions. The areas given over to successive canonical quantities thus typically decline. Full diagnostic shading for a spoke (indicating very surprising changes in expectation) can have very little visual impact for canonical quantities with only small canonical resolutions: mostly we should not be too alarmed about bizarre occurrences in otherwise unimportant directions.