Unformatted text preview: f h1
match (or, the problem
ed text. In other words, the likelihood of getting a match
As Turing was aware, this formulation had two distinct
instruct
ethe logarithm of the independently by Wald shortly after
ver h0 astions was developed ratio of these likelihoods:
an (m )Evidence 1favoring h1 Pr(mahdefinite stoppingthan the
advantages. First, it had  1), was greater time that Pr(on m)
h1 one
given h , denoted / evidence favoring h0
sthe war (Wald, 1947).
log
ch likelihood of getting a match given hwhen to stop working Pr(Second
instructed the codebreaking team , denoted Pr(mh ).
h0m)
0
0
d
As Turing was aware, thisPr(mh1)
formulation had two distinct
he Accordingly, Turing defined the weight of evidence proon one of evidence
1)
Weight pair of ciphers and turn their attention (to another.
log
follows
n
advantages. First, it had aPr(mh0) stopping time that
definite
Second, it predicted the accuracy of the decision,hwhere be h0m
as
Pr( rela
0).
h vided by a match (or, similarly, athe weight ofto stop working
instructed the codebreaking nonmatch) in favor ofcan
team when evidence 1
ofollows. By Bayes’ theorem,
probabilities a
over h0 of the logarithm of the ratio of attention to another.
Bayes probabilities, and probabilities:
ea logarithmasrule:to several this quantity isthese likelihoods:
on one pair Pr(hm) =otherturn their measured
of ciphers Pr(mh)Pr(h)/Pr(m)
s1
be related
h
pothesis after
Pr(
log
).
Second, it predicted of accuracy of the decision, as ) and Pr(h
0s:
units that depend on the basethethe logarithm (Good,
Pr(h0
Pr(
Pr(m of
Pr( 1m)
Pr(hof
o In Banburismus, logarithms 1) base weighthused
follows.hBy Bayes’ theorem, the 10 were 1) evidence describe the p
can
979).
Weight oflog
evidence lweight of evidence, (1)
og
(2)
log
Pr(m actuPr(h0m)
be related to (the Banburismus processh
other
h1 were called “bans” severalPr(h0) probabilities:0)
nd
where
evidence is sa
(1)
s: computed weights of evidence in units of 1/10th of
lly
probab
prior probabili
wherer(Pr(mm) and Pr(h11)m) are called the posterior
P h1 h0of probabilities, this quantity is measured
)
Pr(h
As log
logarithm
ban—a adeciban—that the codebreakers considered
log
weight of evidence, hy(2) pothesi
assumption m
probabilities) and describe) the probability of each
Pr(h0smalleston the baseevidence that is (Good,
m
Pr(h0of of the logarithm
be in units that depend the evidence has been sampled, and
Pr(h a
ed “abou...
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 Spring '08
 LEWIS
 Banburismus

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