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that is, if G captures by u-separation only (conditional) independences that are valid in . G is said to be a perfect map of the conditional (in)dependences in iff it is both a dependence map and an independence map. It is clear that the same notions can be defined for directed acyclic graphs G = (U, E) in exactly the same way, so we do not provide a separate definition. A conditional dependence graph of a distribution guarantees that (sets of) attributes that are not separated in the graph are indeed conditionally dependent in the distribution. It may, however, display dependent (sets of) attributes as separated nodes (or node sets, respectively). Conversely, a conditional independence graph of a distribution guarantees that (sets of) attributes that are separated in the graph are indeed conditionally independent in the distribution. There may be, however, (sets of) conditionally independent attributes that are not separated in the graph. It is obvious that a graph with no edges is a trivial conditional dependence graph and that a complete graph is a trivial conditional independence graph,



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that represent pictorially the songs of two cricket species and of hybrids between them. A comparison of these sonograms reveals that the hybrid songs have features of the songs of both of its parent species, but are distinct from them and from one another. This observation, together with the fact that song is a product of wing-case shape, musculature, and nervous system, suggests strongly that song production in these species is polygenic.

Lerat et al., 2005

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Multiple responses on the same scale (eg, pretest, posttest, and follow-up scores on a measure of depression) are generally considered to produce univariate statistical designs (eg, within-subjects ANOVA), although they are sometimes treated multivariately Having multiple responses complicates data screening because there are also relationships among those responses to consider Examining the Variables or the Residuals of Analysis Another issue is whether the examination of assumptions is performed on the raw variables prior to analysis or whether the main analysis is performed and its residuals examined Both procedures are likely to uncover the same problems For example, a peculiar score (an outlier) can be identi ed initially as a deviant score in its own distribution or as a score with a large residual that is not t well by the solution Temptation is a major difference between these two alternatives.

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Even this simple example poses a number of far-reaching research questions. How does the placement of computational nodes and network connectivity impact the performance of network and application If the computing resources can be arbitrarily chosen within the network, what is the best algorithm to select the CPU and visualization sites Is the network or the CPU congestion more important for scheduling consideration These and other questions are critical architectural considerations, and quantifying some of these factors is essential in determining the interactions between the applications and networks, and the coordination and discovery of Grid resources.

When residuals are examined after the main analysis is performed, the results of the main analysis are also available for inspection If the results are the desired ones, it is tempting to see no problems with the residuals If the results are not the desired ones, it is tempting to begin to play with the variables to see what happens to the results On the other hand, when the assumptions are assessed and decisions are made about how to handle violations prior to the main analysis, there is less opportunity for temptation to in uence the results that are accepted and reported Even if raw variables are screened before analysis, it is usually worthwhile to examine residuals of the main analysis for insights into the degree to which the nal model has captured the nuances of the data.

In what ways does the model fail to t or explain the data Are there types of cases to which the model does not generalize Is further research necessary to nd out why the model fails to t these cases Did the preparatory tests of assumptions fail to uncover violations that are only evident in direct examination of residuals (Wilkinson et al, 1999).

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