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Say I have a linear problemMp=d, where d is our data,pour parameters andMour "observation matrix" (see http://en.wikipedia.org/wiki/Inverse_problem#Linear_inverse_problems). So what we are dealing with is an overdetermined problem.

Now, I have read an example where we have a vector of datadwhose standard deviation we don't know. Then we try and estimate it, and the estimate is given by

[tex]

\sigma ^2 _{estimate} = \frac{1}{N}\sum\limits_i {\left( {d_i - \left( {Mp} \right)_i } \right)^2 }

[/tex]

My question is: How can they estimate the standard deviation like this? Usually we would use the mean, but they use (Mp)_{i}, and I can't quite see why this yields an estimate.

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# Estimating the standard deviation

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