bv_cvxbook_extra_exercises

# Compare the optimal worst case probability pwc with

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ere ai ∈ Rn are known, vi are IID N (0, σ 2 ) random noises, and φ : R → R is an unknown monotonic increasing function, known to satisfy α ≤ φ′ (u) ≤ β, for all u. (Here α and β are known positive constants, with α < β .) We want to ﬁnd a maximum likelihood estimate of x and φ, given yi . (We also know ai , σ , α, and β .) This sounds like an inﬁnite-dimensional problem, since one of the parameters we are estimating is a function. In fact, we only need to know the m numbers zi = φ−1 (yi ), i = 1, . . . , m. So by estimating φ we really mean estimating the m numbers z1 , . . . , zm . (These numbers are not arbitrary; they must be consistent with the prior information α ≤ φ′ (u) ≤ β for all u.) 54 (a) Explain how to ﬁnd a maximum likelihood estimate of x and φ (i.e., z1 , . . . , zm ) using convex optimization. (b) Carry out your method on the data given in nonlin_meas_data.m, which includes a matrix ˆ A ∈ Rm×n , with rows aT , . . . , aT . Give xml , the maximum likelihood estimate of x. Plot your m 1 ˆml . (You can do this by p...
View Full Document

## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

Ask a homework question - tutors are online