Figure 9.20 (page 533):

Uncertainty in activation energy E and rate constant ln k_m versus number of replicated experiments.

Code for Figure 9.20

Text of the GNU GPL.

main.m

%% 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.

alpha = 0.95;
p     = 2;
chisq = chi2inv(alpha,p);
lnk0  = 1;
E     = 100;
Tmin  = 300;
Tmax  = 500;
nTvals = 10;
n0 = 1;
Tmeas    = linspace(Tmin,Tmax,nTvals)';
S = eye(2);
%meanT = 1/(0.5*(1/Tmin+1/Tmax));
meanT = mean(Tmeas);
sets = [1; 2; 5; 100];
nsets = length(sets);
measvar= 1e-3;
measstddev = sqrt(measvar);
for i = 1:nsets
  %%
  %% stack Tmeas on top of itself sets(i) times
  %%
  Tmeasset = kron(ones(sets(i),1), Tmeas);
  ndata = size(Tmeasset,1);
  Tcenter = -1./Tmeasset + 1/meanT;
  X=[ones(ndata,1) Tcenter];
  amat = S*X'*X*S/measvar;
  level = chisq;
  %%
  %% 95% confidence ellipse
  %%
  [x, y] = ellipse (amat, level, 150);
  idx = (i-1)*2+1;
  table(:,idx:idx+1) = [x y];
end
plot (table(:,1), table(:,2), ...
      table(:,3), table(:,4), ...
      table(:,5), table(:,6), ...
      table(:,7), table(:,8));
title ('Figure 9.20')

../../util/common/ellipse.m

%% Copyright (C) 2001, James B. Rawlings and John W. Eaton
%%
%% 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.

%% [x, y, major, minor, bbox] = ellipse (amat, level, n, shift)
%%
%% Given a 2x2 matrix, generate ellipse data for plotting.  The
%% arguments N and SHIFT are optional.  If N is an empty matrix, a
%% default value of 100 is used.

function [x, y, major, minor, bbox] = ellipse (amat, level, n, shift)

  if (nargin < 3)
    n = 100;
  end

  if (isempty (n))
    n = 100;
  end

  if (nargin < 4)
    shift = [0, 0];
  end

  ss = size (shift);

  if (any (ss ~= [1, 2]))
    if (ss == [2, 1])
      shift = shift';
    else
      error ('shift must be a 2-element row vector');
    end
  end

  if (nargin > 1)

    [v, l] = eig (amat / level);

    dl = diag(l);
    if (any (imag (dl)) || any (dl <= 0))
      error ('ellipse: amat must be positive definite');
    end

    %% Generate contour data.

    a = 1 / sqrt (l(1,1));
    b = 1 / sqrt (l(2,2));

    t = linspace (0, 2*pi, n)';

    xt = a * cos (t);
    yt = b * sin (t);

    %% Rotate the contours.

    ra = atan2 (v(2,1), v(1,1));

    cos_ra = cos (ra);
    sin_ra = sin (ra);

    x = xt * cos_ra - yt * sin_ra + shift(1);
    y = xt * sin_ra + yt * cos_ra + shift(2);

    %% Endpoints of the major and minor axes.

    minor = (v * diag ([a, b]))';
    major = minor;

    major(2,:) = -major(1,:);
    minor(1,:) = -minor(2,:);

    t = [1; 1] * shift;

    major = major + t;
    minor = minor + t;

    %% Bounding box for the ellipse using magic formula.

    ainv = inv (amat);
    xbox = sqrt (level * ainv(1,1));
    ybox = sqrt (level * ainv(2,2));

    bbox = [xbox ybox; xbox -ybox; -xbox -ybox; -xbox ybox; xbox ybox];

    t = [1; 1; 1; 1; 1] * shift;
    bbox = bbox + t;

  else
    error ('usage: ellipse (amat, level, n, shift)');
  end

%% endfunction