Showing papers by "Jerome H. Friedman published in 2002"

Cr‐pyrope garnets in the lithospheric mantle 2. Compositional populations and their distribution in time and space

Abstract: [1] Three novel statistical approaches (Cluster Analysis by Regressive Partitioning [CARP], Patient Rule Induction Method [PRIM], and ModeMap) have been used to define compositional populations within a large database (n > 13,000) of Cr-pyrope garnets from the subcontinental lithospheric mantle (SCLM). The variables used are the major oxides and proton-microprobe data for Zn, Ga, Sr, Y, and Zr. Because the rules defining these populations (classes) are expressed in simple compositional variables, they are easily applied to new samples and other databases. The classes defined by the three methods show strong similarities and correlations, suggesting that they are statistically meaningful. The geological significance of the classes has been tested by classifying garnets from 184 mantle-derived peridotite xenoliths and from a smaller database (n > 5400) of garnets analyzed for >20 trace elements by laser ablation microprobe–inductively coupled plasma-mass spectrometry (LAM–ICPMS). The relative abundances of these classes in the lithospheric mantle vary widely across different tectonic settings, and some classes are absent or very rare in either Archean or Phanerozoic SCLM. Their distribution with depth also varies widely within individual lithospheric sections and between different sections of similar tectonothermal age. These garnet classes therefore are a useful tool for mapping the geology of the SCLM. Archean SCLM sections show high degrees of depletion and varying degrees of metasomatism, and they are commonly strongly layered. Several Proterozoic SCLM sections show a concentration of more depleted material near their base, grading upward into more fertile lherzolites. The distribution of garnet classes reflecting low-T phlogopite-related metasomatism and high-T melt-related metasomatism suggests that many of these Proterozoic SCLM sections consist of strongly metasomatized Archean SCLM. The garnet-facies SCLM beneath Phanerozoic terrains is only mildly depleted relative to Primitive Upper Mantle (PUM) compositions. These data emphasize the secular evolution of SCLM composition defined earlier [Griffin et al., 1998, 1999a] and suggest that at least part of this evolutionary trend reflects reworking and refertilization of SCLM formed in the Archean time.

John W. Tukey's work on interactive graphics

Abstract: If there ever was a tool that could stimulate the imagination and profit from the intuition and creativity of John Tukey, it was computer graphics. John always saw graphics a being central to exploratory data analysis: "Since the aim of exploratory data analysis is to learn what seems to be, it should be no surprise that pictures play a vital role in doing it well. There is nothing better than a picture for making you think of questions you had forgotten to ask (even mentally)." Much of his work focused on static displays designed to be easily drawn by hand, but he realized that if one wanted to effectively explore multivariate data, computer graphics would be an ideal tool. PRIM-9, the first program to use interactive, dynamic graphics for viewing and dissecting multivariate data, was conceived by John during a four month visit to the Computation Research Group of the Stanford Linear Accelerator Center in early 1972. PRIM-9 opened up a fundamentally new way of exploring multivariate data. Its basic operations--Picturing, Rotation, Isolation and Masking--have stood the test of time and form the core of numerous follow-on systems.John's experiences with PRIM-9 gave rise to a slew of other ideas for the analysis of multivariate data, many of them not tied to interactive graphics. The most well known of those is "Projection Pursuit"--automatically finding interesting low-dimensional projections of multivariate data by optimizing a projection index. John was also keenly interested in ways of detecting and modeling nonlinear structures in multivariate data which might not be manifest in projections, such as concentration of data near nonlinear lower dimensional manifolds. Many of his proposals exist only in the form of hand-written notes and appear "far out" even today. John's work on Prim-9 and Projection Pursuit lent respectability to computationally oriented, non mathematical research in Statistics. He moved the center of gravity away from an (over)emphasis on mathematical theory to a greater balance between methodology, theory, and applications and thereby helped revitalize the discipline of Statistics.