# doc-cache created by Octave 8.4.0
# name: cache
# type: cell
# rows: 3
# columns: 5
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
stk_example_misc01


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 432
 STK_EXAMPLE_MISC01  Several correlation functions from the Matern family

 The Matern 1/2 correlation function is also known as the "exponential correla-
 tion function". This is the correlation function of an Ornstein-Ulhenbeck pro-
 cess.

 The Matern covariance function tends to the Gaussian correlation function when
 its regularity (smoothness) parameter tends to infinity.

 See also: stk_materncov_iso, stk_materncov_aniso



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
 STK_EXAMPLE_MISC01  Several correlation functions from the Matern family



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
stk_example_misc02


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 761
 STK_EXAMPLE_MISC02  How to use priors on the covariance parameters

 A Matern covariance in dimension one  is considered as an example.  A Gaussian
 prior is used for all three parameters: log-variance, log-regularity  and log-
 inverse-range.  The corresponding parameter estimates are Maximum A Posteriori
 (MAP) estimates or, more precisely, Restricted MAP (ReMAP) estimates.

 Several values for the variance of the prior  are successively considered,  to
 illustrate the effect of this prior variance on the parameter estimates.  When
 the variance is small, the MAP estimate is close to the mode of the prior.  On
 the other hand, when the variance is large,  the prior becomes "flat"  and the
 MAP estimate is close to the ReML estimate (see figure b).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
 STK_EXAMPLE_MISC02  How to use priors on the covariance parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
stk_example_misc03


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
 STK_EXAMPLE_MISC03  How to deal with (known) seasonality



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
 STK_EXAMPLE_MISC03  How to deal with (known) seasonality




# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
stk_example_misc04


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1095
 STK_EXAMPLE_MISC04  Pareto front simulation

 DESCRIPTION

   We consider a bi-objective optimization problem, where the objective
   functions are modeled as a pair of independent stationary Gaussian
   processes with a Matern 5/2 anisotropic covariance function.

   Figure (a): represent unconditional realizations of the Pareto front and
      and estimate of the probability of being non-dominated at each point
      of the objective space.

   Figure (b): represent conditional realizations of the Pareto front and
      and estimate of the posteriorior probability of being non-dominated
      at each point of the objective space.

 EXPERIMENTAL FUNCTION WARNING

    This script uses the stk_plot_probdom2d function, which is currently
    considered an experimental function.  Read the help for more information.

 REFERENCE

  [1] Michael Binois, David Ginsbourger and Olivier Roustant,  Quantifying
      uncertainty on Pareto fronts with Gaussian Process conditional simu-
      lations,  European J. of Operational Research, 2043(2):386-394, 2015.

 See also: stk_plot_probdom2d



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
 STK_EXAMPLE_MISC04  Pareto front simulation



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
stk_example_misc05


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1044
 STK_EXAMPLE_MISC05  Parameter estimation for heteroscedastic noise variance

 DESCRIPTION

    We consider a 1d prediction problem with noisy data, where the variance of
    the noise depends on the input location.

    A simple heteroscedastic model is used, where the only parameter to be
    estimated is a dispersion parameter (the square of a scale parameter).
    More preciesely, the variance of the noise is assumed to be of the form

       tau^2(x) = phi * (x + 1) ^ 2,

    and the dispersion parameter phi is estimated together with the parameters
    of the covariance function.

 EXPERIMENTAL FEATURE WARNING

    This script demonstrates an experimental feature of STK (namely, gaussian
    noise model objects).  STK users that wish to experiment with it are
    welcome to do so, but should be aware that API-breaking changes are likely
    to happen in future releases.  We invite them to direct any questions,
    remarks or comments about this experimental feature to the STK mailing
    list.

 See also: stk_example_kb09



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 76
 STK_EXAMPLE_MISC05  Parameter estimation for heteroscedastic noise variance





