
\subsection{\bf Choice of Importance Sampling}
\subsection{\bf Weight Function --- I}

\begin{slide}
\begin{itemize}
\item We try to choose $q'(x)$ so $f(x)/q'(x)$ has a smaller standard
deviation than $f(x)$.  

\item The best choice is
$$
q'(x) = f(x)
$$
\item which implies

\begin{description}
\item{$\bullet$ 1.} $F(y)$ is constant with zero standard deviation
\item{$\bullet$ 2.} Probability of getting a particular $x$ value is
$\propto q'(x) = f(x)$.  That is, one ``chooses'' $x$ values to
congregate where function $f$ is large.
\end{description}

\item This is, of course, not realistic as to find $q'(x)=f(x)$
requires solving
$$
q(x)=\int^x_a f(x)\,dx
$$
(i.e., solving indefinite integral and that's harder than
definite integral which is $q(b)$).  
\end{itemize}
\end{slide}

