typo on Y_obs to y_obs

fuhaoda · Nov 9, 2018 · 37dd7a8 · 37dd7a8
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diff --git a/MissingData.pdf b/MissingData.pdf
diff --git a/MissingData.tex b/MissingData.tex
@@ -154,7 +154,7 @@
 			\begin{align*}
 		f(Y,M|\theta, \psi) &= f(Y|\theta) f(M|Y,\psi)\\
 		f(y_{obs},m|\theta, \psi)&= \int f(y_{obs}, Y_{mis}|\theta) f(m|y_{obs}, Y_{mis},\psi) d Y_{mis} \\
-		&= f(m|Y_{obs}, \psi) \int f(y_{obs},Y_{mis}|\theta) dY_{mis}\\
+		&= f(m|y_{obs}, \psi) \int f(y_{obs},Y_{mis}|\theta) dY_{mis}\\
 		&\triangleq f(m|y_{obs}, \psi) f(y_{obs}|\theta)
 		\end{align*}
 Remarks: the lower case means the observed value. The $dY_{mis}$ can only be calculated when $M$ is observed. Also, $f(y_{obs}|\theta)$ is not the same pdf as if we only observed iid data, so that we use $\triangleq$ notation instead of regular equal to, because we define  $f(y_{obs}|\theta) = \int f(y_{obs},Y_{mis}|\theta) dY_{mis}$.