Table of contents
|The series is four lectures.
||Thursday 3-4:30pm March 6 & 13, April 10 & 17
||Boalt room 10 (enter from law school courtyard on
upper Bancroft under the Cardoza quotation).
||Anyone is welcome. Participants should have aptitude for reasoning, mathematics, and science.
||As mentioned here; largely from my own work.
||Informal, but please email cbrenner at berkeley dot
edu to reserve a place (and to help me prepare).
Arrive at least by 2:55 to claim your reserved place. ∃ 32 seats
Registration email please
- tell me percentage chance you will come to the first lecture
- how much and what education or expertise you have in mathematics, genetics,
computation, computational biology, incarceration,
or other connection to the subject as described here
||Sufficient mathematical aptitude to understand probability concepts through Bayes’ theorem.
|Homework, grades, credit & required reading
||None, but I will make recommendations where possible. For a start,
see DNA Identification Technology and
APL and my web site.
Safest is probably the very punctual (I'm told)
half-hourly law school shuttle service from the Human Rights
Center at 2850 Telegraph, Berkeley (pay parking lot behind).
That's 1 mile away, so even if you don't see the shuttle as expected at
2:30 for 2:35 departure, walking would probably work.
Alternatively you might find a 2-hour metered spot on upper Bancroft (i.e. essentially in front
of the law school) at that hour, but of course not guaranteed.
Hence if approaching the university from the uphill (=East) side via Piedmont and turning West onto
Bancroft, I would grab any spot I see.
The parking situation is similar on the North side of campus, i.e.
Hearst, which entails a 15 minute walk across campus.
- Background in math & genetics — March 6
Kinship — March 13
- (Forensic) genetics: genetic rules; forensic markers
- Forensic mathematics: models, probability, likelihood ratio, Bayes, in-class exercises,
simple stain matching
- Forensic mathematics tale
Mixed stain analysis — April 10
- Paternity; body ID
- Mass ID, Familial searching
Y & mitochondrial haplotypes — April 17
- The impossible goal: simple but adequate
- History — “exclusion” & “likelihood ratio” methods
- "Continuous" approach
- Fundamental problem — atomic matching probability
- Brenner's Law
Lectures in Forensic Mathematics for the Public
Forensic mathematics means the mathematics of evidence.
In practice the subject is identification through DNA evidence
because that’s what I enjoy and do.
More than any other forensic area DNA identification offers scope for explicit
Emphasis is on the practical but with necessary forays into theory. Examples will come from particular cases or
situations typical in casework, anecdotes from fieldwork and the courtroom.
- General overview and overriding topics
The likelihood principle is the central concept of forensic mathematics.
For example, if dogs are more reliably
stimulated to bark by strangers than by loneliness, then a barking dog is evidence of a stranger (as opposed to
loneliness). Evidence is quantified by the likelihood ratio. Any other way to quantify evidence is either equivalent to
the likelihood ratio or nonsense. For example fingerprint identification traditionally assumes that “match” is proof
positive of identity, which is nonsense. (Fingerprint impressions are neither in theory nor in practice uniquely
DNA identification relies on a convenient biochemical assay that assigns, for any person, a simple profile
consisting in essence of a few dozen small integers. The variety and distribution in the population of those integers is
reasonably well explained by simple principles of genetics and population genetics. Therefore forensic DNA mathematics
rests on basic combinatorial and probability principles — discrete mathematics.
Mathematical models are the bridge from mathematics to the real world of DNA evidence. The rules of genetics are
simple but the consequences can be far from obvious.
- Specific topics
- Stain matching
Suppose the “unknown” DNA observed at a crime scene is also observed in a suspect. How strong is the evidence
that the suspect is the donor?
- Mixed stains
So sensitive is modern DNA biochemical technology that it is almost the rule that crime scene DNA samples will
be a mixture of more than one donor. DNA can be detected from the mere touch of a shooter on a gun, but other
people who touched the gun may also be detected. Mathematically this creates great complication which requires
much gnashing of teeth.
DNA is apt for identification because it not only has the fingerprint-like quality of differing between
individuals, but also as a genetic material allows identification via relatives.
- Many thousands of bodies from the World Trade Center attack, from Balkan wars,
from Latin American bloodshed of various kinds, from Hurricane
Katrina and the two tsunamis,
have been identified using kinship victim identification by comparing an
anonymous body with relatives of missing persons.
— more pedestrian — connects child to biological father.
- Inheritance sometimes comes down to deciding whether a half-sibling relationship exists between a known
heir and a love-child claimant.
- Off-beat applications include twin zygosity determination.
- Mass identification
Mass identification is in part a large-scale application of kinship identification, but in practice there are
many interesting complications due to the tabula rasa state from which many of the identifications start. It’s
like a no-suspect crime investigation. When there is no particular prior suspicion that a body found in the
desert belongs to a particular family who reported someone missing, how do we decide how large a likelihood
ratio is needed for identification?
- Fundamental problem of forensic mathematics:
the evidential value of matching a single (rare) trait
Quantifying the significance of DNA similarity (in any
of the above problems) involves considering the probability of various DNA traits occurring by chance. If
suspect and unknown are both blood type A which type is observed in 262 of 1000 sampled individuals, the naive
idea that 0.262 is the probability of an innocent suspect matching might be close enough for government work.
But suppose the trait is totally unobserved in 1000 reference individuals — as is often the case with some
kinds of DNA evidence. Then how strong is the evidence that the suspect is the donor?
We’ll need actual mathematical thinking for that.
- More topics include
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