

\subsection{\bf 3\hspace{1em} Overview of Estimation}
\subsection{\bf of Parameters}

\begin{slide}
\begin{itemize}
\item So far, we have been concerned with rather straight-forward
(academic) problems involving random variables with known probability
distributions.

\item Now we turn to a fundamental scientific problem:

\item Given some observations $x_1 \ldots x_n$ (= values of a random
variable) of some physical quantity,

\item how do we extract theoretical parameters describing systems we
have observed, and how do we estimate the error in our determination.

\item This will require rather more careful thought as to the relation
of probability theory and the real world.

\item We will first describe the principle of Maximum
Likelihood---everything else can be derived from this.
\end{itemize}
\end{slide}

