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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\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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\centering\hskip1pt\beginpicture 
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\setcoordinatesystem units <.18in,.04in> 
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template from a nonlinear regression model to a robust nonlinear regression 
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model. 
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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 leastsquare 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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\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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\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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\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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\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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\includegraphics[height=3.5in, width=\textwidth]{mcrb350K.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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\setplotsymbol ({\eightrm .}) 
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\setcoordinatesystem units <3.2in,2.5in> 
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