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Forensics and CS

Forensics and CS. Philip Chan. CSI: Crime Scene Investigation. www.cbs.com/shows/ csi / high tech forensics tools DNA profiling Use as evidence in court cases. DNA. Deoxyribonucleic Acid Each person is unique in DNA (except for twins) DNA samples can be collected at crime scenes

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Forensics and CS

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  1. Forensics and CS Philip Chan

  2. CSI: Crime Scene Investigation • www.cbs.com/shows/csi/ • high tech forensics tools • DNA profiling • Use as evidence in court cases

  3. DNA • Deoxyribonucleic Acid • Each person is unique in DNA (except for twins) • DNA samples can be collected at crime scenes • About .1% of human DNA varies from person to person

  4. Forensics Analysis • Focus on loci (locations) of the DNA • Values at the those loci (DNA profile) are recorded for comparing DNA samples. • Two DNA profiles from the same person have matching values at all loci. • More or fewer loci are more accurate in identification? • Tradeoffs? • FBI uses 13 core loci • http://www.cstl.nist.gov/biotech/strbase/fbicore.htm

  5. We do not want to wrongly accuse someone • How can we find out how likely another person has the same DNA profile?

  6. We do not want to wrongly accuse someone • How can we find out how likely another person has the same DNA profile? • How many people are there in the world?

  7. We do not want to wrongly accuse someone • How can we find out how likely another person has the same DNA profile? • How many people are there in the world? • How low the probability needs to be so that a DNA profile is unique in the world?

  8. We do not want to wrongly accuse someone • How can we find out how likely another person has the same DNA profile? • How many people are there in the world? • How low the probability needs to be so that a DNA profile is unique in the world? • Low probability doesn’t mean impossible • Just very unlikely

  9. Disclaimer: Simple Solution • FBI probably uses a more sophisticated method

  10. Review of basic probability • Joint probability of two independent events • P(A,B) = ?

  11. Review of basic probability • Joint probability of two independent events • P(A,B) = P(A) * P(B) • Independent events mean knowing one event does not provide information about the other events • P(Die1=1, Die2=1) • = P(Die1=1) * P(Die2=1) • = 1/6 * 1/6 = 1/36.

  12. Enumerating the events 36 events, each is equally likely, so 1/36

  13. Joint probability • P(Die1=even, Die2=6) = ?

  14. Joint probability • P(Die1=even, Die2=6) • = 1/2 * 1/6 = 1/12 • P(Die1=1, Die2=5, Die3=4) = ?

  15. Joint probability • P(Die1=even, Die2=6) • = 1/2 * 1/6 = 1/12 • P(Die1=1, Die2=5, Die3=4) • = (1/6)3 = 1/216

  16. DNA profile probability • How to estimate?

  17. DNA profile probability • How to estimate? • Assuming loci are independent • P(Locus1=value1, Locus2=value2, ...) • = P(Locus1=value1) * P(Locus2=value2) * ...

  18. DNA profile probability • How to estimate? • Assuming loci are independent • P(Locus1=value1, Locus2=value2, ...) • = P(Locus1=value1) * P(Locus2=value2) * ... • How to estimate P(Locus1=value1)?

  19. DNA profile probability • How to estimate? • Assuming loci are independent • P(Locus1=value1, Locus2=value2, ...) • = P(Locus1=value1) * P(Locus2=value2) * ... • How to estimate P(Locus1=value1)? • a random sample of size N from the population and • find out how many people out of N have value1 at Locus1

  20. Implementation • MyDis.java • matchDNA • returns true if values at all DNA loci match • getProbabilityOfMatch • returns probability of the match assuming values at all loci are independent

  21. Available Data • dnaloci.txt • DNA profile data from FBI used as profiles with known identity • samples.txt • sample DNA profile data for identification • e.g. DNA profiles from the crime scene

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