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GE 331-Lecture 21

# GE 331-Lecture 21 - Likelihood Approach to Hypothesis...

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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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