Multivariate statistics, forensic sciences, spectroscopy, nonparametric statistics, principal component analysis, target factor analysis, bayesian decision theory


A 2009 report published by the National Research Council addressed the need for improvements in the field of forensic science. In the report emphasis was placed on the need for more rigorous scientific analysis within many forensic science disciplines and for established limitations and determination of error rates from statistical analysis. This research focused on multivariate statistical techniques for the analysis of spectral data obtained for multiple forensic applications which include samples from: automobile float glasses and paints, bones, metal transfers, ignitable liquids and fire debris, and organic compounds including explosives. The statistical techniques were used for two types of data analysis: classification and discrimination. Statistical methods including linear discriminant analysis and a novel soft classification method were used to provide classification of forensic samples based on a compiled library. The novel soft classification method combined three statistical steps: Principal Component Analysis (PCA), Target Factor Analysis (TFA), and Bayesian Decision Theory (BDT) to provide classification based on posterior probabilities of class membership. The posterior probabilities provide a statistical probability of classification which can aid a forensic analyst in reaching a conclusion. The second analytical approach applied nonparametric methods to provide the means for discrimination between samples. Nonparametric methods are performed as hypothesis test and do not assume normal distribution of the analytical figures of merit. The nonparametric iv permutation test was applied to forensic applications to determine the similarity between two samples and provide discrimination rates. Both the classification method and discrimination method were applied to data acquired from multiple instrumental methods. The instrumental methods included: Laser Induced-Breakdown Spectroscopy (LIBS), Fourier Transform Infrared Spectroscopy (FTIR), Raman spectroscopy, and Gas Chromatography-Mass Spectrometry (GC-MS). Some of these instrumental methods are currently applied to forensic applications, such as GC-MS for the analysis of ignitable liquid and fire debris samples; while others provide new instrumental methods to areas within forensic science which currently lack instrumental analysis techniques, such as LIBS for the analysis of metal transfers. The combination of the instrumental techniques and multivariate statistical techniques is investigated in new approaches to forensic applications in this research to assist in improving the field of forensic science.


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Graduation Date





Sigman, Michael


Doctor of Philosophy (Ph.D.)


College of Sciences



Degree Program









Release Date

February 2014

Length of Campus-only Access

1 year

Access Status

Doctoral Dissertation (Open Access)


Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic

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Chemistry Commons