IE 300/GE 331 Lecture 21
Negar Kiyavash, UIUC
1
Likelihood Approach to Hypothesis
Testing:
Set-up:
•
Two possible hypotheses H
0
and H
1
•
Likelihood of observing a certain ranges of X under each hypothesis: p
X
(x; H
0
) and
p
X
(x; H
1
)
•
Observation X (in general it is a vector).
To make our life easy in this course we
only deal with scalar observations.
•
Decision rule:
Find a decision rule that maps the realized value of observation x to
one of the hypothesis
•
In our treatment of BHT in this class:
The decision rule divides the observation
space to two subspaces corresponding to 1) Acceptance region of H
0
(also rejection
region of H
1
); 2) Rejection region of H
0
(also acceptance region of H
1
)
Acceptance
Region R
c
Rejection
Region R

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