
\begin{abstract}
\emph{The following are notes from a talk given to the University of Arizona
Department of Mathematics Graduate Probability Seminar on February 14, 2008.}

\begin{itemize}

\item Consider flipping a fair coin 100 times.  The probability space has size
$2^{100}$, which is on the order of $10^{69}$.  Yet we can easily sample from
this space: each event occurs with equal probability $(1/2)^{100}$, and all we
have to do is conduct 100 independent Bernoulli experiments with $p=1/2$.

\item If the coin isn't fair, not all events occur with equal probability.  Yet
it's still easy to sample from this space:  we conduct 100 independent
Bernoulli experiments with $0 \le p \le 1$.

\item Now suppose the coin flips aren't independent --- they have some peer
pressure.  This system is called a \emph{one-dimensional Ising model} and it's
non-trivial to sample from this space.

\end{itemize}

I will describe how the Metropolis-Hastings algorithm allows us to conduct
experiments using such a model.

\emph{This paper is under construction.}
\end{abstract}
