next up previous
Next: Exploring sensitivity for exchangeable Up: Influence diagrams summarising sequential Previous: Generating the diagram

Interpreting the diagram

  figure638
Figure 6:  

How should we interpret the influence diagram shown in Figure 6? Only the path correlation circles shown on arcs entering the G node are new features - the remainder we interpret as described above. For example, examining the outer shadings reveals that the information source tex2html_wrap_inline2283 is expected to explain at least 50% of the variance in each of the individual quantities excepting the intercept C, for which tex2html_wrap_inline2285 also is a valuable information source. Alternatively, for node D, the partial adjustment by tex2html_wrap_inline2285 following an initial adjustment by tex2html_wrap_inline2283 isn't expected to contribute much more to variance resolution.

Examining the diagnostic inner node shadings, we see mostly blue shadings, indicating smaller than expected changes in expectation. In particular, the change for node C induced by observing batch2 is very much smaller than expected. A few of the inner node shadings are red, but not so large as to indicate a serious contradiction between the belief inputs and the actual observations. The same can be said for the overall adjustment summary for the G node: there is an initial slightly larger than expected change in expectation due to observing the first batch; followed by three further diagnostically innocuous adjustments. The outer shadings for the G node suggest that each of the four batches contribute to the explanation of uncertainty across the collection G.

The small circles at the ends of the arcs drawn to the G node represent path correlations between the sources of information. These express the observed degree of concordance between two composite information sources in determining the revision of beliefs. Values near tex2html_wrap_inline2311 indicate that two information sources are complementary: together they give larger changes in belief than would be given by the sum of their individual effects. Conversely, values near tex2html_wrap_inline2313 indicate contradictory evidence, with some consequent cancelling out of their respective changes in belief. We show the magnitude of correlation by degree of shading of the small circle, and direction by colour: light blue for positive, light red for negative. In Figure 4, all the path correlations are positive. Respectively, they are 0.69, 0.97, 0.66, and 0.07. Thus, for example, the information in batch4 is only weakly related to the information carried by the other three batches taken together.


next up previous
Next: Exploring sensitivity for exchangeable Up: Influence diagrams summarising sequential Previous: Generating the diagram

David Wooff
Thu Oct 15 11:27:04 BST 1998