Getting the error "Missing $ inserted" in LaTeX

It's actually the underscores. Use \_ instead, or include the underscore package.

I had this problem too. I solved it by removing the unnecessary blank line between equation tags. This gives the error:

\begin{equation}
P(\underline{\hat{X}} | \underline{Y}) = ...

\end{equation}

while this code compiles succesfully:

\begin{equation}
P(\underline{\hat{X}} | \underline{Y}) = ...
\end{equation}

The "Missing $ inserted" is probably caused by the underscores and bars. These characters in LaTeX have special meaning in math mode (which is delimited by $ characters). Try escaping them; e.g. update\_element instead of update_element.

However, if you're trying to display code, a better solution would be to use the \verb command, which will typeset the text in a monospaced font and will automatically handle underscores and bars correctly (no need to escape them with \).