Statistical Analysis in Forensic Science : Evidential Values of Multivariate Physicochemical Data

338 Pages·2013·15.822 MB·English

by  Grzegorz Zadora, Agnieszka Martyna, Daniel Ramos, Colin Aitken

Grzegorz Zadora Agnieszka Martyna Daniel Ramos Colin Aitken
Statistical Analysis in
Forensic Science
Evidential Value of Multivariate
Physicochemical Data

Statistical Analysis in Forensic Science

Statistical Analysis in
Forensic Science
Evidential Value of Multivariate
Physicochemical Data
Grzegorz Zadora
Institute ofForensicResearch,Krako´w,Poland
Agnieszka Martyna
FacultyofChemistry,JagiellonianUniversity,Krako´w,Poland
Daniel Ramos
EscuelaPolite´cnicaSuperior,UniversidadAutonoma deMadrid,Spain
Colin Aitken
SchoolofMathematics,UniversityofEdinburgh,UK
Thiseditionfirstpublished2014
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Statisticalanalysisinforensicscience:evidentialvalueofmultivariatephysicochemicaldata/GrzegorzZadora,
AgnieszkaMartyna,DanielRamos,ColinAitken.
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ISBN978-0-470-97210-6(cloth)
1.Chemistry,Forensic. 2.Forensicstatistics. 3.Chemometrics. I.Zadora,Grzegorz. II.Martyna,
Agnieszka. III.Ramos,Daniel. IV.Aitken,Colin.
RA1057.S732014
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2013031698
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1 2014
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Contents
Preface xiii
1 Physicochemicaldataobtainedinforensicsciencelaboratories 1
1.1 Introduction 1
1.2 Glass 2
1.2.1 SEM-EDXtechnique 4
1.2.2 GRIMtechnique 5
1.3 Flammableliquids:ATD-GC/MStechnique 8
1.4 Carpaints:Py-GC/MStechnique 10
1.5 Fibresandinks:MSP-DADtechnique 13
References 15
2 Evaluationofevidenceintheformofphysicochemicaldata 19
2.1 Introduction 19
2.2 Comparisonproblem 21
2.2.1 Two-stageapproach 21
2.2.2 Likelihoodratioapproach 23
2.2.3 Differencebetweenanapplicationoftwo-stageapproachand
likelihoodratioapproach 26
2.3 Classificationproblem 27
2.3.1 Chemometricapproach 27
2.3.2 Likelihoodratioapproach 31
2.4 LikelihoodratioandBayes’theorem 31
References 32
3 Continuousdata 35
3.1 Introduction 35
3.2 Datatransformations 37
3.3 Descriptivestatistics 39
3.3.1 Measuresoflocation 39
3.3.2 Dispersion:Varianceestimation 42
3.3.3 Datadistribution 44
3.3.4 Correlation 45
3.3.5 Continuousprobabilitydistributions 49
viii CONTENTS
3.4 Hypothesistesting 59
3.4.1 Introduction 59
3.4.2 Hypothesistestforapopulationmeanforsampleswithknown
varianceσ2fromanormaldistribution 60
3.4.3 Hypothesistestforapopulationmeanforsmallsampleswith
unknownvarianceσ2fromanormaldistribution 63
3.4.4 Relationbetweentestsandconfidenceintervals 67
3.4.5 Hypothesistestbasedonsmallsamplesforadifferenceinthe
meansoftwoindependentpopulationswithunknownvariances
fromnormaldistributions 68
3.4.6 Pairedcomparisons 72
3.4.7 Hotelling’sT2test 75
3.4.8 Significancetestforcorrelationcoefficient 77
3.5 Analysisofvariance 78
3.5.1 PrinciplesofANOVA 78
3.5.2 FeatureselectionwithapplicationofANOVA 82
3.5.3 Testingoftheequalityofvariances 85
3.6 Clusteranalysis 85
3.6.1 Similaritymeasurements 86
3.6.2 Hierarchicalclusteranalysis 89
3.7 Dimensionalityreduction 92
3.7.1 Principalcomponentanalysis 93
3.7.2 Graphicalmodels 99
References 105
4 Likelihoodratiomodelsforcomparisonproblems 107
4.1 Introduction 107
4.2 Normalbetween-objectdistribution 108
4.2.1 Multivariatedata 109
4.2.2 Univariatedata 110
4.3 Between-objectdistributionmodelledbykerneldensityestimation 110
4.3.1 Multivariatedata 111
4.3.2 Univariatedata 111
4.4 Examples 112
4.4.1 Univariateresearchdata–normalbetween-objectdistribution–
Rsoftware 112
4.4.2 Univariatecaseworkdata–normalbetween-objectdistribution–
Bayesiannetwork 116
4.4.3 Univariateresearchdata–kerneldensityestimation–Rsoftware 119
4.4.4 Univariatecaseworkdata–kerneldensityestimation–
calcuLatoRsoftware 125
4.4.5 Multivariateresearchdata–normalbetween-objectdistribution–
Rsoftware 127
4.4.6 Multivariateresearchdata–kerneldensityestimationprocedure–
Rsoftware 129
4.4.7 Multivariatecaseworkdata–kerneldensityestimation–Rsoftware 137