Statistical Detection Theory II

# Statistical Detection Theory II - Detection and...

This preview shows pages 1–6. Sign up to view the full content.

Detection and Estimation (Spring, 2009) Statistical Detection Theory II NCTU EE P.1 Statistical Detection Theory (II) ~ Composite Hypothesis Testing Now we deal with unknown parameters. The pdf under H 0 or under H 1 or under both hypotheses may not be completely specified. Example: DC Level in WGN with Unknown Amplitude (A > 0) The NP detector decides H 1 if The test statistic does not depend on A. Without knowing A, we can still find the NP test.

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

View Full Document
Detection & Estimation (Spring, 2009) Statistical Detection Theory II NCTU EE P.2 However, P D will depend on A. Over all possible detectors that have a given P FA , the NP detectors that decides H 1 if yields the highest P D for any value of A, as long as A > 0. Remark: When this type of test exists, it is called a uniformly most powerful ( UMP ) test. Unfortunately, UMP tests seldom exist.
Detection & Estimation (Spring, 2009) Statistical Detection Theory II NCTU EE P.3 If - < A < , we would obtain different tests for A positive and A negative. if A > 0 if A < 0 Since the value of A is unknown, the NP approach does not result in a unique test. Remark: 9 One-sided test : Two-sided test : 9 For a UMP test to exist, the parameter test must be one-sided. 9 When a UMP test does not exist, we may use the performance of the NP detector as an upper bound. 9 A detector that assumes perfect knowledge of an unknown parameter to design the NP detector is referred to as a clairvoyant detector . Example: DC Level in WGN with Unknown Amplitude When A can take on positive and negative values, the clairvoyant detector decides H 1 if This detector is unrealizable. However, it provides an upper bound on performance. Under H 0 , For A > 0,

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

View Full Document
Detection & Estimation (Spring, 2009) Statistical Detection Theory II NCTU EE P.4 For A < 0, For a constant P FA , we choose γ - = - γ + Under H 1 , For A > 0, For A < 0,
Detection & Estimation (Spring, 2009) Statistical Detection Theory II NCTU EE P.5 For this example, we may try to decide H 1 if For this detector, it can be shown that ~ Composite Hypothesis Testing Approaches Two major approaches to composite hypothesis testing: Bayesian Approach : consider the unknown parameters as realizations of random variables and assign a prior pdf.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.
• Spring '09
• Sheng-JyhWang
• Statistical hypothesis testing, detection theory, Statistical Detection Theory, Statistical Detection Theory II

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern