Correct vhar system equations

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2024-11-12 18:40:55 +01:00
parent 3328d0a3c1
commit 592c0e90df
10 changed files with 39 additions and 35 deletions

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@@ -26,11 +26,11 @@ The \MLE model then predicts that the integrated estimated property $\tilde{s}$
\begin{equation}{MLE}
\tilde{s} = \sum_i w_i \tilde{s}_i \quad \text{with} \quad \sum_i w_i = 1
\end{equation}
Where the individual weights $w_i$ are proportional to their inverse variances:
where the individual weights $w_i$ are proportional to their inverse variances:
\begin{equation}{MLE_weights}
w_i = \frac{1/\sigma_i^2}{\sigma^2}
\end{equation}
And the integrated variance $\sigma^2$ is the inverse of the sum of the individual variances:
and the integrated variance $\sigma^2$ is the inverse of the sum of the individual variances:
\begin{equation}{MLE_variance}
\sigma^2 = \left( \sum_i \frac{1}{\sigma_i^2} \right)^{-1}
\end{equation}