A common theme is to try to evaluate the complexity

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Unformatted text preview: at when X = 4 or X = 5, the ML rule decides that a one was transmitted, not a zero, but because zeroes are so much more likely to be transmitted than ones, the MAP rule decides in favor of a zero in this case. Example 2.11.3 (Sensor fusion) Two motion detectors are used to detect the presence of a person in a room, as part of an energy saving temperature control system. The first sensor outputs a value X and the second sensor outputs a value Y . Both outputs have possible values {0, 1, 2}, with larger numbers tending to indicate that a person is present. Let H0 be the hypothesis a person is absent and H1 be the hypothesis a person is present. The likelihood matrices for X and for Y are shown: H1 H0 X=0 X=1 X=2 0.1 0.3 0.6 0.8 0.1 0.1 H1 H0 Y =0 Y =1 Y =2 0.1 0.1 0.8 0.7 0.2 0.1 For example, P (Y = 2|H1 ) = 0.8. Suppose, given one of the hypotheses is true, the sensors provide conditionally independent readings, so that P (X = i, Y = j |Hk ) = P (X = i|Hk )P (Y = j |Hk ) for i, j ∈ {0, 1, 2} and k ∈ {0, 1}. (a) Find...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

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