this is for holding javascript data
Anisha Keshavan added Thanks_for_catching_this_The__.tex
over 8 years ago
Commit id: ae3909fd8f81d0180253d15967d806043d5c4c41
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Thanks for catching this! The formulas are now:
\begin{equation} \label{mle} L_1 = \prod\limits_j\frac{1}{\sqrt{2\pi a_j^2 V_j}}exp\Big(\frac{-(\beta_{1j}- \mu)^2}{2 a_j^2 V_j}\Big) \end{equation}
and
\begin{multline} \frac{\partial}{\partial \mu}\Big(log(L_1)\Big) = \frac{\partial}{\partial \mu} \Big(\sum\limits_j^J \frac{1}{\sqrt{2 \pi a_j^2 V_j}} + \sum\limits_j^J \frac{(\beta_{1j} - \mu)^2}{2 a_j^2V_j}\Big) = 0 \implies \hat{\mu} = \frac{\sum\limits_j^J a_j^{-2}V_j^{-1}\beta_{1j}}{\sum\limits_j^J a_j^{-2}V_j^{-1}} \end{multline}
