Statistical DNA Forensics Book

Preface     xi
List of figures     xiii
List of tables     xvii
Introduction     1
Statistics, forensic science and the law     1
The use of statistics in forensic DNA     1
Genetic basis of DNA profiling and typing technology     3
Genetic basis     3
Typing technology     4
About the book     5
Probability and statistics     7
Probability     7
Dependent events and conditional probability     9
Law of total probability     10
Bayes' Theorem     11
Binomial probability distribution     12
Multinomial distribution     13
Poisson distribution     14
Normal distribution     14
Likelihood ratio     16
Statistical inference     17
Test of hypothesis     17
Estimation and testing     19
Problems     20
Population genetics     23
Hardy-Weinberg equilibrium     23
Test for Hardy-Weinberg equilibrium     25
Observed and expected heterozygosities     25
Chi-square test     27
Fisher's exact test     29
Computer software     30
Other statistics for analysis of a population database     31
Linkage equilibrium     31
Power of discrimination     33
DNA profiling     35
Subpopulation models     37
Relatives     42
Problems     45
Parentage testing     47
Standard trio     47
Paternity index     47
An example     48
Posterior odds and probability of paternity     49
Paternity computer software     52
Steps in running the software     52
The software to deal with an incest case     52
A relative of the alleged father is the true father     54
Alleged father unavailable but his relative is     57
Motherless case     58
Paternity index     58
Computer software and example     59
Motherless case: relatives involved     60
A relative of the alleged father is the true father     60
Alleged father unavailable but his relative is     62
Computer software and example     62
Determination of both parents     63
Probability of excluding a random man from paternity      66
Power of exclusion     68
A random man case     68
A relative case     69
An elder brother case: mother available     71
Other issues     74
Reverse parentage     74
Mutation     75
Problems     76
Testing for kinship     79
Kinship testing of any two persons: HWE     79
Computer software     83
Kinship testing of two persons: subdivided populations     83
Joint genotype probability     83
Relatives involved     87
Examples with software     89
Three persons situation: HWE     91
Computer software and example     95
Three persons situation: subdivided populations     96
Standard trio     96
A relative of the alleged father is the true father     97
Alleged father unavailable but his relative is     99
Example     99
General method and computer software     101
Complex kinship determinations: method and software     102
EasyPA_In_1_Minute software and the method     104
EasyPAnt_In_1_Minute     107
EasyIN_In_1_Minute      107
EasyMISS_In_1_Minute     108
Other considerations: probability of paternity and mutation     110
Problems     111
Interpreting mixtures     113
An illustrative example     113
Some common cases and a case example     115
One victim, one suspect and one unknown     115
One suspect and two unknowns     116
Two suspects and two unknowns     117
Case example     118
Exclusion probability     119
A general approach     121
Population in Hardy-Weinberg equilibrium     122
Population with multiple ethnic groups     124
Subdivided population     128
Single ethnic group: simple cases     128
Single ethnic group: general situations     128
Multiple ethnic groups     132
Computer software and example     134
NRC II Recommendation 4.1     135
Single ethnic group     135
Multiple ethnic groups     137
Proofs     141
The proof of Equation (6.6)     141
The proof of Equation (6.8)     142
The proof of Equation (6.9)     142
The proofs of Equations (6.11) and (6.12)      142
The proofs of Equations (6.14) and (6.15)     145
Problems     145
Interpreting mixtures in the presence of relatives     147
One pair of relatives: HWE     147
Motivating example     148
A probability formula     149
Tested suspect with an unknown relative     150
Unknown suspect with a tested relative     151
Two related persons were unknown contributors     152
An application     153
Two pairs of relatives: HWE     157
Two unknowns related respectively to two typed persons     159
One unknown is related to a typed person and two other unknowns are related     160
Two pairs of related unknowns     161
Examples     161
Extension     165
Related people from the same subdivided population     165
Introductory example     165
A simple case with one victim, one suspect and one relative     167
General formulas     167
An example analyzed by the software     170
Proofs     172
Preliminary     172
The proof of Equation (7.5)     180
The proof of Equation (7.7)     180
The proof of Equation (7.9)      181
The proof of Equation (7.11)     181
The proof of Equation (7.13)     181
The proofs of Equations (7.18) and (7.20)     181
Problems     186
Other issues     187
Lineage markers     187
Haplotypic genetic markers for mixture     189
Bayesian network     191
Peak information     194
Mass disaster     196
Database search     197
Solutions to problems     201
The standard normal distribution     225
Upper 1% and 5% points of x[superscript 2] distributions     227
Bibliography     229
Index     237