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L. Billard 331FIGURE 29.5PCA based on intervals.u = 10; thus, the principal component hypercube is larger for u =5thanforu = 10. That is, the observation u = 5 has a larger internal variation. Theseinternal variations are a component of the covariance terms in the covariance(and correlation) matrix. This feature is not possible in a classical analysis,with the point observation in R p being transformed into but a point value inPC-space, as shown in Figure 29.6 for the classical principal component analysisperformed on the interval means. While both the symbolic and classicalanalyses showed the temperatures as being of comparable importance to PC 1with elevation being important only for PC 2 ,thevisualizationsthroughthePC hypercubes of Figure 29.5 are more informative than are the PC points ofFigure 29.6.29.4 ConclusionBy the time that Eddy (1986) considered the future of computers in statisticalresearch, it was already clear that a computer revolution was raising its headover the horizon. This revolution was not simply focussed on bigger and bettercomputers to do traditional calculations on a larger scale, though that too wasa component, then and now. Rather, more expansively, entirely new ways ofapproaching our art were to be the new currency of the looming 21st century.Early signs included the emergence of new methodologies such as the bootstrap(Efron, 1979) and Gibbs sampler (Geman and Geman, 1984), thoughboth owed their roots to earlier researchers. While clearly these and similarcomputational methodologies had not been feasible in earlier days thereby beinga product of computer advances, they are still classical approaches per se.