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Forensic Analysis Weighing Bullet Lead Evidence (2004) / Chapter Skim
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Appendix H: Principal Components Analysis: How Many Elements Should Be Measured?
Pages 157-162

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From page 157...
... Recall that the equivalence t test requires specification of a value SIRE where RE = relative error and a value ~ denoting the expected probability of a false match. Each simulation run would use a different combination of the elements: there are 35 possible subsets of three of the seven elements, 35 possible subsets of four of the seven elements, 21 possible subsets of five of the seven elements, seven possible subsets of six of the seven elements, and one simulation run corresponding to using all seven elements.
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From page 158...
... The corresponding variances in order of increasing percentages are found in Tables H.2, H.4, H.6, andH.8. This calculation may not directly relate to results obtained by simulating the false match probability as described above, but it does give some indication of the contribution of the different elements, and the results appear to be consistent with the impressions of the scientists who have been measuring bullets and making comparisons (Ref.
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From page 159...
... Bi, Ag, and Cd, respectively. Row labels 1, 2, and 3 represent the first principal components through third, and the rows show the total variation due to each successive element included in the subset.
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From page 160...
... Bi, Ag, and Cd, respectively. Row labels 1, 2, 3, and 4 represent the first principal component through fourth, and the rows show the total variation due to each successive element included in the subset.
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From page 161...
... Bi, Ag, and Cd, respectively. Row labels 1, 2, 3, 4, and 5 represent the first principal components through fifth, and the rows show the total variation due to each successive element included in the subset.
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From page 162...
... Row labels 1, 2, 3, 4, 5, and 6 represent the first principal component through sixth, and the rows show the total variation due to each successive element included in the subset. 2 3 4 5 6 7 1234567 77.64703 104.24395 124.20241 132.33795 134.94053 136.60234 136.94360 Summary: 3 elements: 4 elements: 5 elements: 6 elements: 237 1237 12357 123567 7 elements: 1234567 (83.6% of total variance)
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Key Terms

  • principal components
  • components analysis
  • total variation
  • match probability
  • false match

  • successive element
  • increasing variance
  • variation due
  • row labels
  • element included

  • seven elements
  • principal component
  • lowest false
  • measuring bullets
  • directly relate

  • various choices
  • similar process
  • testing purposes
  • results appear
  • data set

  • total variability
  • linear combinations
  • simulation run
  • variation using
  • subset containing

  • linear combination
  • results obtained
  • subset pca
  • elemental calculations
  • subset accounts


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