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The values û and v ^ that minimize (7) is the ordinary least squares regression solution when predicting t ˜ i from b ˜ i and g ˜ i. Moreover the estimate of αt i in each position i is obtained as the residual of the regression for that positions value, i.e. t ^ i = t ˜ i - n ^ i and the estimates are easily calculated using any software library that offers least squares regression modelling.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com