GE 331-Lecture 20

GE 331-Lecture 20 - Two hypotheses: The radar receiver is...

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IE 300/GE 331 Lecture 20 Negar Kiyavash, UIUC 1 Two hypotheses: • The radar receiver is attempting to decide whether a target is present or not • The target may be present or it may not • The receiver is thus considering two hypotheses about the state of affairs •H 0 : the hypothesis that a target is absent •H 1 : the hypothesis that a target is present • Only one of these hypotheses is true
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IE 300/GE 331 Lecture 20 Negar Kiyavash, UIUC 2 Truth versus What I believe is true • The receiver announces -H 0 is the true hypothesis -or ±H 1 is the true hypothesis • The announcement (a.k.a. the decision) may or may not coincide with reality • Distinguish between what is the truth and what
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IE 300/GE 331 Lecture 20 Negar Kiyavash, UIUC 3 Binary Hypothesis Testing: Terminology • The case with only two hypotheses H 0 and H 1 is a very important special case •H 0 is called the null hypothesis •H 1 is called the alternative hypothesis • The alternative hypothesis is the one that we are trying to establish, e.g. target is present • The null hypothesis is the default condition
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IE 300/GE 331 Lecture 20 Negar Kiyavash, UIUC 4 Binary Hypothesis Testing: Terminology • Rejecting the alternative may not be the same as accepting the null hypothesis • The alternative is rejected if there is not sufficient evidence to support it • It may be that neither hypothesis is true and the truth lies elsewhere (except when the null hypothesis is formulated as the complement of the alternative hypothesis) • People are often careless in formulating the statements of the hypotheses
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IE 300/GE 331 Lecture 20 Negar Kiyavash, UIUC 5 Example: • Example of testing a coin to determine if it is a biased coin
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GE 331-Lecture 20 - Two hypotheses: The radar receiver is...

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