Figure 9.18:

Effect of next measurement temperature on parameter confidence intervals.

Code for Figure 9.18

Text of the GNU GPL.

main.m


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% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License as
% published by the Free Software Foundation; either version 2, or (at
% your option) any later version.
%
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
% General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; see the file COPYING.  If not, write to
% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
% MA 02111-1307, USA.

chisq = 5.99;  % chi square value for 95% confidence level with 2 parameters
lnk0  = 1;
E     = 100;
Tmin  = 300;
Tmax  = 500;
nTvals = 3;
n0 = 1;
T0    = [ones(n0,1)*Tmin; ones(n0,1)*Tmax];
S = eye(2);
Trep  = [300, 500, 1000];
meanT = 1/(0.5*(1/Tmin+1/Tmax));
table = [];
for i = 1:length(Trep)
  Tmeas = [T0; Trep(i)];
  ndata = size(Tmeas,1);
  Tcenter = -1./Tmeas + 1/meanT;
  X=[ones(ndata,1) Tcenter];
  measvar= 1e-3;
  measstddev = sqrt(measvar);
  amat = S*X'*X*S/measvar;
  level = chisq;
  %
  % volume of 95% confidence ellipse and bounding box
  %
  inva = inv(amat);
  intun(i) = sqrt(level*inva(1,1));
  slopeun(i) = sqrt(level*inva(2,2));
  vol(i) = pi*level/(sqrt(det(amat)));
  vbox(i) = 4*level*sqrt(prod(diag(inva)));
  [x, y] = ellipse (amat, level, 150);
  table = [table x y];
end
save -ascii nextT.dat table;

if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
plot (table(:,1), table(:,2), ...
       table(:,3), table(:,4), table(:,5), table(:,6));
% TITLE
end % PLOTTING