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Unformatted text preview: hat the two objective values can be interpreted
as meansquare estimation error E x − x 2 .
ˆ
2
6.8 Optimal detector design. We adopt here the notation of §7.3 of the book. Explain how to design a
(possibly randomized) detector that minimizes the worstcase probability of our estimate being oﬀ
by more than one,
ˆ
Pwc = max prob(θ − θ ≥ 2).
θ (The probability above is under the distribution associated with θ.)
Carry out your method for the problem instance with data in off_by_one_det_data.m. Give the
⋆
optimal detection probability matrix D. Compare the optimal worstcase probability Pwc with the
ml
worstcase probability Pwc obtained using a maximumlikelihood detector.
6.9 Experiment design with condition number objective. Explain how to solve the experiment design
problem (§7.5) with the condition number cond(E ) of E (the error covariance matrix) as the
objective to be minimized.
6.10 Worstcase probability of loss. Two investments are made, with random returns R1 and R2 . The
total return for the two investments is R1...
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 Fall '13
 F.Borrelli
 The Aeneid

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