1% STK_EXAMPLE_KB10  Leave-one-out (LOO) cross validation
2%
3% This example demonstrate the use of Leave-one-out (LOO) cross-validation to
4% produced goodness-of-fit graphical diagnostics.
5%
6% The dataset comes from the "borehole model" response function, evaluated
7% without noise on a space-filling design of size 10 * DIM = 80.  It is analyzed
8% using a Gaussian process prior with unknown constant mean (with a uniform
9% prior) and anisotropic stationary Matern covariance function (regularity 5/2;
10% variance and range parameters estimated by restricted maximum likelihood).
11%
12% See also stk_predict_leaveoneout, stk_plot_predvsobs, stk_plot_histnormres
13
14% Copyright Notice
15%
16%    Copyright (C) 2016 CentraleSupelec
17%
18%    Author:  Julien Bect  <julien.bect@centralesupelec.fr>
19
20% Copying Permission Statement
21%
22%    This file is part of
23%
24%            STK: a Small (Matlab/Octave) Toolbox for Kriging
25%               (http://sourceforge.net/projects/kriging)
26%
27%    STK is free software: you can redistribute it and/or modify it under
28%    the terms of the GNU General Public License as published by the Free
29%    Software Foundation,  either version 3  of the License, or  (at your
30%    option) any later version.
31%
32%    STK is distributed  in the hope that it will  be useful, but WITHOUT
33%    ANY WARRANTY;  without even the implied  warranty of MERCHANTABILITY
34%    or FITNESS  FOR A  PARTICULAR PURPOSE.  See  the GNU  General Public
35%    License for more details.
36%
37%    You should  have received a copy  of the GNU  General Public License
38%    along with STK.  If not, see <http://www.gnu.org/licenses/>.
39
40stk_disp_examplewelcome ();
41
42% Define the input domain (see stk_testfun_borehole.m)
43BOX = stk_hrect ([                                 ...
44    0.05   100  63070  990  63.1 700 1120  9855;   ...
45    0.15 50000 115600 1110 116   820 1680 12045],  ...
46    {'rw', 'r', 'Tu', 'Hu', 'Tl', 'Hl', 'L', 'Kw'});
47
48% Generate dataset
49d = size (BOX, 2);
50x = stk_sampling_maximinlhs (10 * d, d, BOX);   % Space-filling LHS of size 10*d
51y = stk_testfun_borehole (x);                % Obtain the responses on the DoE x
52
53% Build Gaussian process model
54M_prior = stk_model (@stk_materncov52_aniso, d);  % prior
55M_prior.param = stk_param_estim (M_prior, x, y);  % ReML parameter estimation
56
57% Compye LOO predictions and residuals
58[y_LOO, res_LOO] = stk_predict_leaveoneout (M_prior, x, y);
59
60% Plot predictions VS observations (left planel)
61%  and normalized residuals (right panel)
62stk_figure ('stk_example_kb10 (a)');  stk_plot_predvsobs (y, y_LOO);
63stk_figure ('stk_example_kb10 (b)');  stk_plot_histnormres (res_LOO.norm_res);
64
65% Note that the three previous lines can be summarized,
66% if you only need the two diagnostic plots, as:
67%
68%    stk_predict_leaveoneout (M_prior, x, y);
69%
70% (calling stk_predict_leaveoneout with no output arguments creates the plots).
71