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Talk:Inverse-variance weighting

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Confusing symbols in the Multivariate case section

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The notation used in the section on the multivariate case is quite confusing, in the that the is used to indicate both a sum and a covariance matrix. Additionally, the symbol is used to denote a covariance matrix, whereas in the rest of the article is used to mean variance.

I have boldly edited the equations to use the more common symbol for covariance matrices. The older formulae are retained below.


of the individual estimates :

— Preceding unsigned comment added by Glopk (talkcontribs) 16:11, 8 September 2023 (UTC)[reply]

Derivation from maximum likelihood?

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Let there be a set of measurements , each with uncertainty , of a variable . A "gaussian" probability distribution function of with respect to each measurment is:

The log-likelihood of given the measurements, ( could be multiplied with -1, doesn't matter):

Finding that maximizes likelihood should give the "best" estimator of the weighted-mean of the values, taking the uncertainties into account:

So then, from the above the "best" is:

Decomposing the variance of , we get:

Blakut (talk) 08:52, 14 June 2023 (UTC)[reply]