Re: Drift in plotting of confidence region ellipsoid

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Ravi mutturi 2016-5-12

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/283858-re-drift-in-plotting-of-confidence-region-ellipsoid

I am trying to plot the confidence region ellipsoid using following code for a (3x3) covariance matrix into 3 seperate 2-dimensional plots with midpoints [16.4083;96.9713;9.4083]. However my confidence ellipsoids are having drift from the above midpoints. I am assuming chisquare distribution with 95%confidence region. Kindly help.

covar_matrix=[  88.5333  -33.6000   -5.3333
             -33.6000   15.4424    2.6667
              -5.3333    2.6667    0.4848];
 cov_m1m2 =   [88.5333  -33.6000
  -33.6000   15.4424];
cov_m2m3 = [15.4424    2.6667
  2.6667    0.4848];
cov_m1m3 = [88.5333     -5.3333
  -5.3333        0.4848];
mL2m1m2 = [16.4083
  96.9713];
mL2m2m3 = [96.9713
  9.4083];
mL2m1m3 = [16.4083
  9.4083];
m1=-50:2.44:50;
m2=80:1:120;
m3=7:0.122:12;
chi_1 = zeros(41,41);
chi_2 = zeros(41,41);
chi_3 = zeros(41,41);
for j=1:1:41
  for i=1:1:41
      p_5 = m1(i);
      p_6 = m2(j);
      mtrue =[p_5 p_6]';
      p_4 = mtrue - mL2m1m2;
      epp = (p_4'/cov_m1m2)*p_4;
      chi_1(i,j) = chi2pdf(epp,2);
      if chi_1(i,j) > 5.9915
          chi_1(i,j) = 5.9915;
      end
      %chi_1(i,j) = chi2inv(0.95,chi_a);
      clear p4 p5 p6 epp
  end
end
clear i j
for j=1:1:41
  for i=1:1:41
      p_5 = m2(i);
      p_6 = m3(j);
      mtrue =[p_5 p_6]';
      p_4 = mtrue - mL2m2m3;
      epp = (p_4'/cov_m2m3)*p_4;
      chi_2(i,j) = chi2pdf(epp,2);
      if chi_2(i,j) > 5.9915
          chi_2(i,j) = 5.9915;
      end
      %chi_2(i,j) = chi2inv(0.95,chi_a);
      clear p4 p5 p6 epp
  end
end
clear i j
for j=1:1:41
  for i=1:1:41
      p_5 = m1(i);
      p_6 = m3(j);
      mtrue =[p_5 p_6]';
      p_4 = mtrue - mL2m1m3;
      epp = (p_4'/cov_m1m3)*p_4;
      chi_3(i,j) = chi2pdf(epp,2);
      if chi_3(i,j) > 5.9915
          chi_3(i,j) = 5.9915;
      end
      clear p4 p5 p6 epp
  end
end
clear i j
chi_1;
x_cord_1 = m1;
x_cord_2 = m2;
x_cord_3 = m3;
[X_1,X_2] = meshgrid(x_cord_1,x_cord_2);
figure
hold on
Z_1 = chi_1;
subplot(3,1,1);
contour(X_1,X_2,Z_1)
[X_2,X_3] = meshgrid(x_cord_2,x_cord_3);
Z_2 = chi_2;
subplot(3,1,2);
contour(X_2,X_3,Z_2)
[X_1,X_3] = meshgrid(x_cord_1,x_cord_3);
Z_3 = chi_3;
subplot(3,1,3);
contour(X_1,X_3,Z_3)