bv_cvxbook_extra_exercises

The name derives from the fact that t is proportional

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Unformatted text preview: hat the two objective values can be interpreted as mean-square 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 worst-case 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 worst-case probability Pwc with the ml worst-case probability Pwc obtained using a maximum-likelihood 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 Worst-case 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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