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Pattern Recognition by Matthias Nagel, Matthias Richter, Jürgen Beyerer

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In order for the estimator to be unbiased, the expected value must be equal to the true value, which gives

E{ σ 2 ^ }= σ 2 N αN =1α=2N.

(4.6)The expected value of the estimator ̂μ is

E{ σ 2 ^ }= σ 2 N αN =1α=2N.

It is unbiased if

E{ σ 2 ^ }= σ 2 N αN =1α=2N.

A.5Chapter 5

(5.1)The inverse mapping x= A 1 ( y )=± y is not unique, therefore the inference from y to x is ill-posed.

(5.2)The system of equations to solve this problem is over-determined, since there are more data points (N < 2) than degrees of freedom (a,b). This means that in general there is no solution that interpolates all data points. Therefore, the problem is ill-posed.

The following variation is well-posed.

Find the parameters ...

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