Changeset 1760 for trunk/doc/pslib/psLibADD.tex

Timestamp:

Sep 9, 2004, 10:17:05 AM (22 years ago)

Author:

Paul Price

Message:

Commented out the section on confidence limits, since it was not
relevant, but we may want to include it in the future.

File:

• trunk/doc/pslib/psLibADD.tex (modified) (2 diffs)

trunk/doc/pslib/psLibADD.tex

@@ -1 @@
-%%% $Id: psLibADD.tex,v 1.44 2004-09-09 02:42:10 price Exp $
+%%% $Id: psLibADD.tex,v 1.45 2004-09-09 20:17:05 price Exp $
 \documentclass[panstarrs]{panstarrs}
 
@@ -503 +503 @@
 distributed, the formal errors on the parameters are then calculated
 by setting $\lambda = 0$ and calculating the covarience matrix
-$C_{i,j}$, the inverse of the matrix $\alpha_{j,k}$.  The independent
-68.3\% confidence limit on parameter $a_k$ is then $\sqrt{C_{k,k}}$.
-Confidence contours for sets of parameters may be defined as well by
-the function $\Delta = \delta\bar{a} P_{j,k}^{-1} \delta\bar{a}$ where
-$P_{j,k}$ is the projected matrix of $C_{j,k}$, ie those rows and
-columns of $C_{j,k}$ associated with the parameters of interest, the
-vector $\delta\bar{a}$.  The value of $\Delta$ is given by the table
-below for specific confidence limits and numbers of parameters.  
-Note that it is necessary to be able to calculate both the function as
-well as its derivative for any combination of parameters and dependent
-variables.
-
-\begin{center}
-\begin{tabular}{|l|r|r|r|}
-\hline
-{\bf P} & \multicolumn{3}{c|}{\bf $N_{par}$} \\
-        & 1    & 2    & 3    \\
-\hline
-68.3\%  & 1.00 & 2.30 & 3.53 \\
-95.4\%  & 4.00 & 6.17 & 8.02 \\
-99.73\% & 9.00 & 11.8 & 14.2 \\
-\hline
-\end{tabular}
-\end{center}
+$C_{i,j}$, the inverse of the matrix $\alpha_{j,k}$.
+%
+The covariance matrix allows simple calculation of the confidence
+limits of the parameters.
+
+%The independent 68.3\% confidence limit on parameter $a_k$ is then
+%$\sqrt{C_{k,k}}$.  Confidence contours for sets of parameters may be
+%defined as well by the function $\Delta = \delta\bar{a} P_{j,k}^{-1}
+%\delta\bar{a}$ where $P_{j,k}$ is the projected matrix of $C_{j,k}$,
+%ie those rows and columns of $C_{j,k}$ associated with the parameters
+%of interest, the vector $\delta\bar{a}$.  The value of $\Delta$ is
+%given by the table below for specific confidence limits and numbers of
+%parameters.  Note that it is necessary to be able to calculate both
+%the function as well as its derivative for any combination of
+%parameters and dependent variables.
+%
+%\begin{center}
+%\begin{tabular}{|l|r|r|r|}
+%\hline
+%{\bf P} & \multicolumn{3}{c|}{\bf $N_{par}$} \\
+%        & 1    & 2    & 3    \\
+%\hline
+%68.3\%  & 1.00 & 2.30 & 3.53 \\
+%95.4\%  & 4.00 & 6.17 & 8.02 \\
+%99.73\% & 9.00 & 11.8 & 14.2 \\
+%\hline
+%\end{tabular}
+%\end{center}