17HypothesisTesting - Hypothesis Testing Jeffrey B Burl EE...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 3180 Probability and Random  Signal Analysis,  © 2009 by J. B. Burl 1 Hypothesis Testing Jeffrey B. Burl
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
EE 3180 Probability and Random  Signal Analysis,  © 2009 by J. B. Burl 2 Binary Detection: The Source There are two hypotheses:  H 0  and  H 1 One of these hypotheses is true. We will assume the source is random  and generates hypotheses with the  probabilities: P ( H 0 ) P ( H 1 )
Image of page 2
EE 3180 Probability and Random  Signal Analysis,  © 2009 by J. B. Burl 3 The Cost of Failure A decision rule can be either correct or  incorrect, leading to four possible outcomes: D 0  and  H 0  (Decide  H 0  and  H 0  true)   Correct D 1  and  H 0  (Decide  H 1  and  H 0  true)   Incorrect D 1  and  H 1  (Decide  H 1  and  H 1  true)   Correct D 0  and  H 1  (Decide  H 0  and  H 1  true)   Incorrect Assign a cost to every hypothesis-decision  combination: C 00 C 10 C 11 , and  C 01 C ik  is the cost incurred when we decide  H i  ( D i ) and  H k  is true.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
EE 3180 Probability and Random  Signal Analysis,  © 2009 by J. B. Burl 4 The Average Cost The expected value of the cost (the  average cost in the book) is 00 0 0 10 1 0 ( and ) ( and ) C C P D H C P D H = + 11 1 1 01 0 1 ( and ) ( and ) C P D H C P D H + +
Image of page 4
EE 3180 Probability and Random  Signal Analysis,  © 2009 by J. B. Burl 5 The Average Cost, Cont. The probability that we decide  H 0  ( D 0 ) and  H 1   is true can be expanded in terms of the  source probability and the conditional  probability: The average cost can then be written: 0 1 1 0 1 ( and ) ( ) ( | ) P D H P H P D H = 00 0 0 0 10 0 1 0 ( ) ( | ) ( ) ( | ) C C P H P D H C P H P D H = + 11 1 1 1 01 1 0 1 ( ) ( | ) ( ) ( | ) C P H P D H C P H P D H + +
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
EE 3180 Probability and Random  Signal Analysis,  © 2009 by J. B. Burl 6 The Average Cost, Cont. The conditional probability on the previous  slide is a function of the probabilistic  transition mechanism and the decision rule. We would like to separate these two effects to  simplify computation of this conditional  probability.
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern