Figure 9.10:

Distribution of estimated parameters.

Code for Figure 9.10

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.

%
% arhenius.m
%
chisq = 5.99;  % chi square value for 95% confidence level with 2 parameters
lnk0  = 1;
E     = 100;
ndata = 10;
Tmin  = 300;
Tmax  = 500;
Tmeas = linspace(Tmin,Tmax,ndata)';
X     = [ones(ndata,1) -1./Tmeas];
lnk   = X*[lnk0; E];
k     = exp(lnk);
measvar= 1e-3;
measstddev = sqrt(measvar);
%
% set seed for "reproducible" random numbers
%
rng(0);
%
%just a few noisy points
%
nexpts = 500;
clear lnkmeas;
for i = 1:nexpts lnkmeas(:,i) = lnk + measstddev*randn(ndata,1); end
%for i = 1:nexpts kmeas(:,i) = k + measstddev*randn(ndata,1); end
%lnkmeas = log(kmeas);
theta = (inv(X'*X)*X' * lnkmeas)';

%save_precision=5;
%save -ascii arrhenius.dat rest;
%
%center the data first
%
Tcenter = -1./Tmeas + 1/mean(Tmeas);
Xcenter=[ones(ndata,1) Tcenter];
thetacenter = (inv(Xcenter'*Xcenter)*Xcenter' * lnkmeas)';

npts = 181;
amat = X'*X/measvar;
level = chisq;
[x, y, major, minor, bbox] = ellipse (amat, level, npts);
x = x+lnk0;
y = y+E;
minor(:,1)=minor(:,1)+lnk0;
minor(:,2)=minor(:,2)+E;
major(:,1)=major(:,1)+lnk0;
major(:,2)=major(:,2)+E;
bbox(:,1)=bbox(:,1)+lnk0;
bbox(:,2)=bbox(:,2)+E;

tmp = [x, y];

save arrhenius.dat theta bbox tmp;


if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
plot (theta(:,1), theta(:,2), '+', bbox(:,1), bbox(:,2), ...
       tmp(:,1), tmp(:,2));
% TITLE
end % PLOTTING