Abstract:
Forensic DNA analysis has received much public attention over the last thirty years
because of its incredible usefulness in criminal investigations. It has also had considerable
scientific scrutiny, mainly in response to changes in science and legal challenges. The field
of statistics is paramount in DNA evidence interpretation because of the intrinsic
probabilistic nature of the problem. Statistical DNA interpretation uses knowledge from
the fields of: statistics, population genetics, and molecular biology. This has been in
existence for longer than any of the current technologies used for typing the evidence,
because the same basic ideas generally apply, regardless of how the evidence is typed.
In a typical criminal case, biological materials such as blood, semen, saliva, or other body
tissues, may be recovered and between 50 to 100 picograms (10-12g) of DNA is extracted
from these materials for polymerase chain reaction (PCR) amplification. PCR amplification
allows length variants in the DNA, called short tandem repeats (STRs), to be detected by
measuring relative fluorescence when the sample is exposed to laser light. The resulting
signal is collected by a photomultiplier and displayed graphically as an electropherogram
(epg). The epg consists of a trace signal displayed on a molecular weight axis, which is
mostly flat with peaks in various locations. The presence of a peak corresponds to the
alleles present in the DNA sample. Crudely, alleles are variants or polymorphisms of a
gene, which can be used to describe differences between individuals. The heights of the
peaks are approximately proportional to the amount of template DNA present. This
quantitative information (as opposed to the discrete allele information) can greatly
enhance the interpretation process.
The likelihood ratio (LR) approach is (now) the favoured method for presenting forensic
evidence in the court in many jurisdictions. It links the evidence related to two
hypotheses: prosecution and defence. The prosecution hypothesis claims that the accused
is the donor of recovered DNA from the crime scene while the defence claims that an
unknown person who is not blood-related to the accused is the donor. Then the ratio
between the probabilities of the two hypotheses is defined as LR. There are four
competing models: classical, binary, semi-continuous, and continuous for the
interpretation of DNA evidence, which essentially differ in the definitions of the weights
assigned to sets of possible genotypes. Implementing continuous probabilistic models
which ensure relatively greater objectivity and consistency between analysts requires
statistical models for PCR phenomena such as stutter. This research reviews the existing
models and develops new, advanced, Bayesian models for predicting stutter with
increased accuracy. The models include nonhierarchical, hierarchical, and infinite mixture
models.
