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22S:138
The Likelihood Principle
Lecture 22
Nov. 28, 2005
Kate Cowles
374 SH, 335-0727
kcowles@stat.uiowa.edu
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The likelihood principle
•Suppose that two different experiments may
inform about an unknown parameter θ
•Suppose the outcomes of the experiements
are respectively y∗and z∗
•Suppose the likelihoods for θresulting from
the two experiements are proportional; that
is
p(y∗;θ) = c p(z∗;θ)
where c is a constant
•Then the information about θcontained in
both experiments is equivalent
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Another way to state the likelihood prin-
ciple
•For a given sample of data, any two proba-
bility models p(y|θ) that have the same like-
lihood function yield the same inference for
θ.
•With regard to the information contained in
the data about the unknown parameter(s),
only the actual observed data yis relevant.
–No other possible outcomes
∗Contrast this with the frequents p-value
the probability assuming H0is true, of
getting a test statistic as extreme as, or
more extreme than, the value that was
actually obtained
–Not the researchers’ intentions
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Example
•We are given a coin. We are interested in
estimating θ, the probability of obtaining a
head on a single flip.
•We want to test the hypotheses:
H0:θ=1
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Ha:θ > 1
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•Experiment consists of flipping coin 12 times
independently.
•Result is 9 heads and 3 tails.
