I fixed the int32 issue.

As for the references, they've been behaving strangely.  The way you're
suggesting was giving me problems before so I switched it to labeling after
the figure and it worked.  However, it seems to be working where you're
suggesting now so let's go with that.  Changes have been made.


On Wed, May 22, 2013 at 5:53 PM, Ian Henriksen <notifications@github.com>wrote:

> In Algorithms/MarkDecProc/Bandits.tex:
>
> > +R(a_1,b_1,a_2,b_2)
> > +\end{equation}
> > +\noindent
> > +where $a_i$ is the number of successful pulls on arm $i$ and $b_i$ is the number of unsuccessful pulls on arm $i$.
> > +
> > +As we pull the arms, we must balance between pulling the arm that has the highest expected payoff and pulling all arms in order to gain information about the probabilities $p_i$.  This trade-off is often referred to as exploring versus exploiting.  In essence, while gaining rewards, we will also come up with estimates of the $p_i$ that improve our decision making.  We will do so by Bayesian Updating.
> > +
> > +\section*{Bayesian Updating}
> > +While a full exposition of Bayesian inference is well beyond the scope of this lab, the essential concepts are fairly straightforward.  We recognize that we do not know the values of the $p_i$, but given our past history of successful and unsuccessful pulls we can say something about what range we think they might be in. This is different than guessing a specific value for the $p_i$.  For example the value of $p_i$ might be represented by a curve like those seen in Figure \ref{fig:priors}.
> > +
> > +\begin{figure}
> > +\begin{center}
> > +        \includegraphics[width=\textwidth]{./Algorithms/MarkDecProc/priors.pdf}
> > +        \caption{Bayesian priors}
> > +\end{center}
> > +\end{figure}\label{fig:priors}
>
> I guess I should be more precise. I mean this should read
>
> \caption{Bayesian priors}
> \label{fig:priors}
>
> \end{center}
> \end{figure}
>
> —
> Reply to this email directly or view it on GitHub<https://github.com/byuimpact/numerical_computing/pull/96/files#r4351783>
> .
>