

\subsection{\bf What Happens If You Miscalculate}
\subsection{\bf Maximum Weight in}
\subsection{\bf Accept/Reject Approach}

\begin{slide}
\begin{itemize}
\item It is possible to cope with an $f\left(\underline{x}\right) >$
guessed $\max_{\underline{x}} \,f(x)$ in two ways.

\begin{description}
\item{$\bullet$} 1. Weight event with factor $w\left(\underline{x}\right)$ 
in integrand
\[ 
w\left(\underline{x}\right) = \frac{f\left( \underline{x} 
\right)}{\max_{\underline{x}}\,
f\left( \underline{x} \right) \Big\vert_{\rm\, guess}}
\]

\item{$\bullet$} 2. Accept 
\[ 
\frac{f\left( \underline{x} 
\right)}{\max_{\underline{x}}\,
f\left( \underline{x} \right) \Big\vert_{\rm\, guess}}
\]
copies of $\underline{x}$.  
\end{description}

\item This approach (2.) is possible even if not an integer using
probability to accept $>1$ particles!
\end{itemize}
\end{slide}

