I am trying to plot the experimental confidence regions that is 1 sigma, 2 sigma etc for a data which consists of experimental values of two quantities and corresponding delta chi square. So for the below mentioned sample data
I have tried this
x = Function[a, ArcSin[Sqrt[a]]*(180/\[Pi])]@
Import["C:\\Desktop\\data1.txt", {"Data", \
{All}, {1}}];
y = Import[
"C:\\Desktop\\data1.txt", {"Data", {All}, \
{2}}];
data = {x, y}\[Transpose];
deltaChisq =
Import["C:\\Desktop\\data1.txt", {"Data", \
{All}, {3}}];
(*define error Ellipse*)
ErrorEllipse[data_, percLevel_, points_: 100] :=
Module[{eVa, eVec, coors, dchi, thetaGrid, ellipse,
rEllipse}, {eVa, eVec} = Eigensystem@Covariance[data];
(*Get the coordinates of the data mean*)coors = Mean[data];
(*Get the perc[%] confidence interval error ellipse*)
dchi = \[Sqrt]Quantile[deltaChisq, percLevel/100];
(*define error ellipse in x and y coordinates*)
thetaGrid = Table[i, {i, 0, 2 \[Pi], 2 \[Pi]/99}];
ellipse = {dchi \[Sqrt]eVa[[1]] Cos[thetaGrid],
dchi \[Sqrt]eVa[[2]] Sin[thetaGrid]};
(*rotate the ellipse and center ellipse at coors*)
rEllipse = coors + # & /@ (ellipse\[Transpose].eVec)];
(*visualize results*)
percentOneSigma = 66.3;
percentTwoSigma = 95.4;
Show[ListPlot[data],
ListLinePlot[ErrorEllipse[data, percentOneSigma],
PlotStyle -> {Thick, Red}],
ListLinePlot[ErrorEllipse[data, percentTwoSigma],
PlotStyle -> {Thick, Blue}],
ListPlot[{Mean[data]}, PlotStyle -> {Thick, Red}],
ListLinePlot[ErrorEllipse[data, 99.7], PlotStyle -> {Dotted, Black}],
PlotRange -> All]
Which giving me some ellipses, but I think they are not the exact confidence ellipses. Since this is a non linear data it should be a isocontour having constant chi square values. The contour should be the 2D 2 variable contour like this ![][1]
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