Program on Statistics and Applied Mathematics in Forensic Science (Forensics)

Forensics-Microscope-SmForensic science uses scientific principles and methods to analyze materials collected at crime scenes, in order to connect these materials to suspects. According to the Locard exchange principle, every contact will cause a transfer of material. Thus, criminals leave material at crime scenes. Forensic scientists investigate this material.

Forensic science is, in major part, based upon statistical comparisons of the characteristics of a material left at a crime scene to characteristics of a source or suspect. These comparisons are often acknowledged by forensic scientists to be highly subjective. Indeed, some forensic scientists deny the need for statistics. For example in firearm/toolmarks, they many testify that ‘they do not need the science of statistics because they don’t use numbers.

Over the past several years, the National Research Council (NRC) has convened committees that have raised deep questions about major forms of forensic evidence, including:

  • Bullet lead: “the bullet recovered from the victim matches the bullets found in the suspect’s house’’ (NRC, 2004).
  • Ballistic evidence: “the marks on the bullet recovered at the crime scene match the suspect’s gun” (NRC, 2008).

The 2009 NRC report Strengthening Forensic Science in the United States: A Path Forward makes a clear case for a needed statistical underpinning for forensic procedures, including fingerprints, patterns and impressions (footprints and tire tracks), toolmarks and firearms, hair, fibers, documents, paints and coatings, bloodstains, and fire debris.

For example, in regard to friction ridge analyses (fingerprints) the NRC writes “To properly underpin the process of friction ridge identification, additional research is also needed into ridge flow and crease pattern distributions on the hands and feet. This information could be used to limit the possible donor population of a particular print in a statistical approach and could provide examiners with a more robust understanding of the prevalence of different ridge flows and crease patterns. Additionally, more research is needed regarding the discriminating value of the various ridge formations and clusters of ridge formations. This would provide examiners with a solid basis for the intuitive knowledge they have gained through experience and provide an excellent training tool. It also would lead to a good framework for future statistical models and provide the courts with additional information to consider when evaluating the reliability of the science. Recently, research has begun to build some of this basis [emphases added].”

The need for increased presence of mathematical techniques and mathematical underpinnings has also been documented elsewhere. There have been 316 DNA exonerations in the United States. Presently, unvalidated and improper forensic science has contributed to approximately half of all DNA exonerations. According to the NAS report, “Many of the processes used in the forensic science disciplines are largely empirical applications of science—that is, they are not based on a body of knowledge that recognizes the underlying limitations of the scientific principles and methodologies used for problem solving and discovery. It is therefore important to focus on ways to improve, systematize, and monitor the activities and practices in the forensic science disciplines and related areas of inquiry. Thus, in this report, the term “forensic science” is used with regard to a broad array of activities, with the recognition that some of these activities might not have a well-developed research base, are not informed by scientific knowledge, or are not developed within the culture of science.”(p. 39)

Thus, forensic science is data-driven. The central goal of this program is to strengthen the statistical and applied mathematical bases of forensic science.

Forensics Working Groups

Multiple Sources of Bias
Working Group Leaders: Sandy Zabell, Cliff Spiegelman

Pattern Evidence
Working Group Leaders: Karen Kafadar, Anil Jain

Forensic Data Bases
Working Group Leader: Dennis Lin

Shoeprints as Evidence
Working Group Leaders: Cliff Spiegelman, Sarena Wiesner

Possible Matches
Working Group Leader: Len Stefanski

Ballistic Images
Working Group Leaders: Nell Sedransk, Cliff Spiegelman

Forensic Evidence
Working Group Leader: Cedric Neumann


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Additional information on each group can be found at Working Groups.

Questions: email forensics@samsi.info