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Bias correction in weighted variance
For unweighted variance
$$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$
there exists the bias corrected sample variance, when the mean was estimated from the same data:
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Weighting datapoints by uncertainty - asymmetric CIs
I have several estimates obtained using different softwares, these programs give me an estimate as well as a 95% confidence interval. However, these CIs are not symmetric around my point estimates, ...