The code in Figure 3 produces the influence diagram shown in Figure 4. Note that this diagram is generated from a colour postscript file produced directly from [B/D]; its translation into a monochrome image results in gray scale shadings which make the different colours hard to distinguish. For the inner node shading, the heavier shading corresponds to blue, and the lighter shading corresponds to red. The inner node of node D contains examples of both. Note also that all the features portrayed on the influence diagram are available as standard output, via the SHOW: command, as described in [15]. Table 2 contains all of the information summarised on the influence diagram.
The two sources of information (Y and Z)
are drawn in the centre of the diagram. Nodes for the individual random
quantities 
are drawn on the right, and the node
representing their collection, G, is drawn on the left. Directed
arcs are drawn from the information sources to the nodes
being adjusted to represent information flow. We called for the arcs to
node C to be labelled. Various features of the
adjustment are shown by (1) shading of the outer node; (2) shading of
the inner node; (3) shading of the arc half label nearest the source
node, and of the arc half label nearest the destination node.
. For the single adjustment of node 
by
node 
, we shade the corresponding part of the outer sector,
starting at 
degrees and working counter-clockwise. The shading
is in the same colour as the information source (and the arc connecting
the two nodes) to aid identification of important contributory
information sources. Consider for example the adjustment of the
intercept term C by the information collection Y. C has prior
variance 1.0, and adjusted variance 0.7720, a resolution of
. Consequently, 22.8% of the outer sector is
shaded. The remaining 77.2% represents variation (or uncertainty) in
C unexplained by Y.
The extra shading of the outer node expresses the portion of the remaining
uncertainty in C that is explained by further fitting on the information
source Z. This extra resolution is about 57.0% of prior, so that the
overall fit by both Y and Z resolves 
of the
uncertainty, leaving
20.2% of original variation in C unexplained by either Y or Z. The
adjustment by Z in addition to the adjustment by Y is called
a partial adjustment. The variance explained by Z alone is not
shown by node shading.
, so that
the actual change in expectation is about 1.7 standard deviations larger
than expected. As a result, the inner sector for this adjustment is
roughly half shaded red.
For the partial adjustment of C by the extra information source Z,
having taken into account Y, the corresponding size ratio is
. Thus, not only is the contribution to
variance reduction attributable to Z over and above Y substantial,
but also the associated actual changes in expectation attributable to
the partial adjustment are surprisingly large. Hence a substantial portion
of the corresponding inner sector is shaded red.
,
informally the information ``leaving'' and (ii) the loss in
variance reduction that would result if the node were
withdrawn from the overall adjustment, informally the information
``arriving'' at from I. As for node shadings, each variance
resolution is associated with a diagnostic measure comparing expected to
actual behaviour.
To illustrate, we have drawn two labels on the arcs connecting Y and
Z to C. The information leaving node 
for node 
is
summarised in the half label nearer the node , whereas the
information arriving at from is summarised in the half
label nearer the node . We consider each half separately as
representing 100% of the prior variance in the destination node.
We partition the half label nearest Y into (1) the proportion of
variance in C explained by the overall fit, 
; (2) the proportion of variance in C explained by
alone, 
. A portion of the latter is then
shaded to depict the diagnostic measure. (As we adjusted firstly by Y,
these half-label shadings correspond exactly to the node C shadings
for the first adjustment. This will not be the case for the half-label
shadings for information sources used in subsequent adjustments, such as
Z here.)
We partition the half label nearest C into (1) the proportion of
variance in C explained by the overall fit, ; (2) the proportion of explained variance in C lost by
withdrawing the information source alone. This is a useful
measure in the sense of parsimonious fitting, as some information
sources might be found to be redundant as all their explanatory power
is carried by other information sources. In this example, the only other
information source is Z, and it alone explains about 75.2% of the
variance in C. Consequently, the loss in explanation of variance when
Y is removed from the overall fit is 
of prior.
The value 4.6% is indicated on the influence diagram by a vertical
line, giving a bar of width 4.6% which indicates the information
arriving at C from Y. As before, a portion of this bar is now shaded
to depict the standard diagnostic measure (the size ratio for the
adjustment with Y extracted is 
standard deviations; somewhat larger changes in expectation than
expected).
In conclusion, this label shows that for an appreciable amount of
information leaves Y, but very little arrives. In each case, the
associated standardised changes in expectation are rather larger than
expected. If we do not have access to the information source Z,
Y alone has some potential to reduce uncertainty in C.
Otherwise, if Z is available, Y is not additionally valuable as it
can contribute only an extra 4.6% variance reduction.
The influence diagram facilitates rapid appraisal of features of adjustments over complex stochastic structures. Suppose that we return to Figure 4 and review the main features. For the individual terms A,B,C,D most of the variance is explained by Y, Z together, as indicated by outer node shading. In each case, Y (magenta) is the first information source fitted, followed by Z (light green). Clearly Y is more informative for A,B and Z is more informative for C,D, as would be expected from the model (1), but Y singly is also quite informative for C,D, and Z for A,B. Both intercept terms A,C are associated with rather larger changes in expectation than were anticipated (indicated by red shading of the inner nodes) from both information sources. For the slope terms B,D, changes in expectation were less surprising: principally, the change in expectation for D from fitting on Y was rather less than expected. For the overall collection G, it is clear that both information sources are valuable, and that both lead to rather larger than expected changes in expectation.
For other than trivial examples, an initial graphical review of a complex system is followed by further graphical and numerical focussing on particular aspects to which we have been directed by our various diagnostic tools. In this way, we deconstruct the complex system into smaller manageable areas, pursuing the anomalies exhibited by the influence diagrams to whatever level of detail is necessary to unravel and comprehend surprising features of the adjustment process. For example, we have seen some rather larger than expected changes in expectation, indicating potentially serious conflicts between data and belief specifications. Here, we might begin by examining the model at the element (random quantity) level, to try to localise and identify contradictory features.
