Revision 1077 trunk/docs/manuals/admb/admb.tex

admb.tex (revision 1077)
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regression procedures. Further discussion about the underlying theory can be
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found in the \scAD\ user's manual, but it is not necessary to understand the
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theory to make use of the procedure.
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\begin{figure}[h]
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\begin{figure}[htbp]
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  \centering\hskip1pt\beginpicture
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  \setcoordinatesystem units <.18in,.04in>
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  \setplotarea x from 0 to 16.5, y from 0 to 50
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analysis. An alternative approach, which avoids these difficulties, is to employ
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\ADM's robust regression procedure, which removes the undue influence of
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outlying points without the need to expressly remove them from the data.
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\begin{figure}[h]
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\begin{figure}[htbp]
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  \centering\hskip1pt\beginpicture
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    \setcoordinatesystem units <.18in,.04in>
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    \setplotarea x from 0 to 16.5, y from 0 to 50
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template from a nonlinear regression model to a robust nonlinear regression
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model.
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\begin{figure}[h]
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\begin{figure}[htbp]
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\centering\hskip1pt\beginpicture
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  \setcoordinatesystem units <.18in,.04in>
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  \setplotarea x from 0 to 16.5, y from 0 to 50
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better than least-square estimates in the presence of moderate or large
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outliers. You can lose only a little and you stand to gain a lot by using these
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estimators.
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\begin{figure}[h]
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\begin{figure}[htbp]
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\centering\hskip1pt\beginpicture
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  \setcoordinatesystem units <.18in,.04in>
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  \setplotarea x from 0 to 16.5, y from 0 to 50
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concentrations of the reactants are known only approximately.
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See~Table~\ref{tab:runs} for what they are.
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%xx \htmlbegintex
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\begin{table}[h]
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\begin{table}[htbp]
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\begin{center}
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\begin{tabular}{@{\extracolsep{1em}} l c  l}
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 \bf Run 1&$s_1(0)=\theta_5=1\pm0.05$&$s_2(0)=\theta_6=1\pm0.05$\\
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produced this way. Also, a plot of $y_i$ versus $x_i$ gives the user an
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indication of what the probability distribution of the parameter looks like.
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(See Figure~\ref{fig:05}.)
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\begin{figure}[h]
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\begin{figure}[htbp]
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\centering\hskip1pt\beginpicture
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    \setplotsymbol ({\eightrm .})
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  %\setcoordinatesystem units <.7in,5in> Have to adjust so labels don't overlap.
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the estimates produced by the \textsc{mcmc} method, for different sample sizes
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(25,000 and 2,500,000 samples) for the \texttt{catage} example.
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%xx \htmlbeginignore
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\begin{figure}[h]
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\begin{figure}[htbp]
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%xx \htmlendignore
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\centering\hskip1pt\beginpicture
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  \setplotsymbol ({\eightrm .})
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standard deviations fixed. The number \texttt{N} should be between~1 and~9. The
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smaller the number, the more the correlation is reduced. For this example (see
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Figure~\ref{fig:07}), a value of~3 seemed to perform well.
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\begin{figure}[h]
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\begin{figure}[htbp]
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\includegraphics[height=3.5in, width=\textwidth]{mcrb3-50K.png}
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\emptycaption
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\label{fig:07}
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The plot of \texttt{qa} and \texttt{qb} demonstrates the extra information about
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the probability distribution of the current state contained in in the current
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value of~\texttt{y(t)}. (See Figure~\ref{fig:08}.)
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\begin{figure}[h]
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\begin{figure}[htbp]
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\centering\hskip1pt\beginpicture
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  \setplotsymbol ({\eightrm .})
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  \setcoordinatesystem units <3.2in,2.5in>

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