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Unformatted text preview: t the after all weight
evidence is0)eq
pothesis
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1979). In Banburismus, Pr(h m) of called were used
irectly perceptible htom) ) andlogarithmsare base 10 the posterior
human called the prior probabilities and
intuition”; Good, 1979).
describ
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posterior prob
where and Pr(h1 are
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1 robabilities and describe the probability of each hyh
instructed the codebreaking team when to stop working
othesison oneall the evidence has been sampled, and
after pair of ciphers and turn their attention to another.
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Background: Banburismus of the and
). h0) and Pr(h1) it predictedthe prior probabilitiesdecision, as
Second, are called the accuracy at Bletchley Park
escribefollows. By Bayes’ problem weight of evidence can
the probability of theorem, the
each hypothesis before any
Formalize the
vidence isrelated to severalexample, there is an equal
be sampled. If, for other probabilities:
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rior probability of either hypothesis (which was the
:
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Pr(h1)
ssumption madem) Banburismus), then theof evidence, (2)
weight of
log
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log
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vidence is equalm) the logarithm of the ratio of the
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osterior probabilities. In this case, for a given weight
ifwhere knowledge is equal 1for the two hypothesis
prior Pr(h0m) and Pr(h m) are called the posterior
f evidence (e.g., the stopping point in Banburismus):
probabilities and describe the probability of each hypothesis m) all the evidence has been sampled, and
after
Pr(h1
eight of evidence B
(3)
log h0) and Pr(h1)ware called the prior probabilities and
,
Pr( Pr(h m)
0
describe the probability of each hypothesis before any
here Bevidence is sampled. If, for example, there is an equal
is a constant that represents the barrier height
h1 is1 true two of How much the hypotheses
f favor prior .probabilitymutually exclusive evidence favors theover h0
either hypothesis (which was h1
of h For
1
Pr( 1m) in Banburismus), then 1
r(h0m)assumptionhmadeor, equivalently, Pr(h0) the weight of
s(h )), and assuming the to the logarithm of the ratio of the
evidence is equal weight of evidenc...
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