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% STK_EXAMPLE_KB10 Leave-one-out (LOO) cross validation
%
% This example demonstrate the use of Leave-one-out (LOO) cross-validation to
% produced goodness-of-fit graphical diagnostics.
%
% The dataset comes from the "borehole model" response function, evaluated
% without noise on a space-filling design of size 10 * DIM = 80. It is analyzed
% using a Gaussian process prior with unknown constant mean (with a uniform
% prior) and anisotropic stationary Matern covariance function (regularity 5/2;
% variance and range parameters estimated by restricted maximum likelihood).
%
% See also stk_predict_leaveoneout, stk_plot_predvsobs, stk_plot_histnormres
% Copyright Notice
%
% Copyright (C) 2016 CentraleSupelec
%
% Author: Julien Bect <julien.bect@centralesupelec.fr>
% Copying Permission Statement
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (http://sourceforge.net/projects/kriging)
%
% STK 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 3 of the License, or (at your
% option) any later version.
%
% STK 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 STK. If not, see <http://www.gnu.org/licenses/>.
stk_disp_examplewelcome ();
% Define the input domain (see stk_testfun_borehole.m)
BOX = stk_hrect ([ ...
0.05 100 63070 990 63.1 700 1120 9855; ...
0.15 50000 115600 1110 116 820 1680 12045], ...
{'rw', 'r', 'Tu', 'Hu', 'Tl', 'Hl', 'L', 'Kw'});
% Generate dataset
d = size (BOX, 2);
x = stk_sampling_maximinlhs (10 * d, d, BOX); % Space-filling LHS of size 10*d
y = stk_testfun_borehole (x); % Obtain the responses on the DoE x
% Build Gaussian process model
M_prior = stk_model (@stk_materncov52_aniso, d); % prior
M_prior.param = stk_param_estim (M_prior, x, y); % ReML parameter estimation
% Compye LOO predictions and residuals
[y_LOO, res_LOO] = stk_predict_leaveoneout (M_prior, x, y);
% Plot predictions VS observations (left planel)
% and normalized residuals (right panel)
stk_figure ('stk_example_kb10 (a)'); stk_plot_predvsobs (y, y_LOO);
stk_figure ('stk_example_kb10 (b)'); stk_plot_histnormres (res_LOO.norm_res);
% Note that the three previous lines can be summarized,
% if you only need the two diagnostic plots, as:
%
% stk_predict_leaveoneout (M_prior, x, y);
%
% (calling stk_predict_leaveoneout with no output arguments creates the plots).
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