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CATEGORIES:Statistics
SUMMARY:What is the chance that the match is coincidence?
- Richard Gill\, Leiden University
DTSTART;TZID=Europe/London:20130524T160000
DTEND;TZID=Europe/London:20130524T170000
UID:TALK45268AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/45268
DESCRIPTION:I'd like to talk about two topics both connected t
o forensic statistics on\nwhich I have been workin
g recently. The 2010 UK Court of Appeal Ruling kno
wn\nas "R v T" asserted that Bayes' theorem and li
kelihood ratios should not be\nused in evaluating
forensic evidence\, except for DNA and 'possibly o
ther\nareas where there is a firm statistical base
'. This illustrates that the\ntask of communicatin
g the evidential value of statistical evidence to
a\ncourt is not easy.\n\nThe first\, more mathemat
ical\, main topic\, is the subject of an ongoing\n
collaboration with Dragi Anevski (Lund). Think of
it as a nonparametric\nmissing data estimation pro
blem with parameter restricted by ordering\nconstr
aints. \n\nConsider a probability distribution ove
r an infinite set. Let p=(p_1\,p_2\,?)\nbe the vec
tor of all the atoms of this probability distribut
ion ordered from\nlarge to small and augmented wit
h zero's if there are only finitely many\natoms. N
ow take an iid sample of size n from this distribu
tion\, count how\noften each element is observed\,
and similarly order the resulting counts\nfrom la
rge to small. This results in our observed data Y=
(Y_1\,Y_2\,?). The\nproblem we are interested in i
s how to estimate the underlying vector of\nordere
d probabilities p from the observed vector of orde
red counts Y. Note\nthat the k'th most frequent el
ement in the sample is not necessarily the\nk'th m
ost frequent element in the population!\n\nI will
discuss our preliminary results on the nonparametr
ic maximum\nlikelihood estimator of p\, which is v
ery different from the naieve estimator\nY/n\, and
explain their relevance to the problem of evaluat
ing the evidential\nvalue of a rare Y-chromosome m
atch - a problem called "the fundamental\nproblem
of forensic mathematics" by Charles Brenner (Berke
ley).\n\nThe second topic concerns the problem of
deciding whether or not two mobile\ntelephones act
ually belong to the same person\, based on call re
cords (times\nof calls\, locations of GSM towers)
of both of the phones. Here there is no\nsimple mo
del and no simple mathematical problem to be solve
d\, but on the\nother hand an equally challenging
problem of how the statistician can advise\na cour
t on the evidential value of the evidence. The cou
rt in question will\nbe the United Nations Special
Tribunal on Lebanon\, the crime is the\nassassina
tion of premier Rafiq Hariri in 2005.\n
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:Richard Samworth
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