# doc-cache created by Octave 4.0.0
# name: cache
# type: cell
# rows: 3
# columns: 9
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb01


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 558
 STK_EXAMPLE_KB01  Ordinary kriging in 1D

 A Matern covariance function is used for the Gaussian Process (GP) prior. The
 parameters of this covariance function are assumed to be known (i.e., no
 parameter estimation is performed here).

 The word 'ordinary' indicates that the mean function of the GP prior is
 assumed to be constant and unknown.

 The example first performs kriging prediction based on noiseless data (the
 kriging predictor, which is the posterior mean of the GP model, interpolates
 the data in this case) and then based on noisy data.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
 STK_EXAMPLE_KB01  Ordinary kriging in 1D



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb02


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 513
 STK_EXAMPLE_KB02  Ordinary kriging in 1D with parameter estimation

 We consider an ordinary kriging approximation in 1D: the mean function of the
 Gaussian process prior is assumed to be constant and unknown. A Matern covari-
 ance function is used, and its parameters are estimated using the Restricted
 Maximum Likelihood (ReML) method.

 The example can be run either with noisy data  or with noiseless (exact) data,
 depending on the value of the NOISY flag (the default is false, i.e., noise-
 less data).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
 STK_EXAMPLE_KB02  Ordinary kriging in 1D with parameter estimation



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb03


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 543
 STK_EXAMPLE_KB03  Ordinary kriging in 2D

 An anisotropic Matern covariance function is used for the Gaussian Process
 (GP) prior. The parameters of this covariance function (variance, regularity
 and ranges) are estimated using the Restricted Maximum Likelihood (ReML)
 method.

 The mean function of the GP prior is assumed to be constant and unknown. This
 default choice can be overridden by means of the model.order property.

 The function is sampled on a space-filling Latin Hypercube design, and the
 data is assumed to be noiseless.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
 STK_EXAMPLE_KB03  Ordinary kriging in 2D



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb04


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 734
 STK_EXAMPLE_KB04  Estimating the variance of the noise

 This example constructs an ordinary kriging approximation in 1D, with
 covariance parameters and noise variance estimated from the data.

 A Matern covariance function is used for the Gaussian Process (GP) prior. The
 parameters of this covariance function are estimated using the Restricted
 Maximum Likelihood (ReML) method.

 The mean function of the GP prior is assumed to be constant and unknown.

 In this example, the variance of the observation noise is not assumed to be
 known, and is instead estimated from the data together the parameters of the
 covariance function. This is triggered by the used of the fifth (optional)
 argument in the call to stk_param_estim.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 55
 STK_EXAMPLE_KB04  Estimating the variance of the noise



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb05


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 948
 STK_EXAMPLE_KB05  Generation of conditioned sample paths

 A Matern Gaussian process model is used, with constant but unknown mean
 (ordinary kriging) and known covariance parameters.

 Given noiseless observations from the unknown function, a batch of conditioned
 sample paths is drawn using the "conditioning by kriging" technique. In short,
 this means that unconditioned sample path are simulated first (using
 stk_generate_samplepaths), and then conditioned on the observations by kriging
 (using stk_conditioning).

 Note: in this example, for pedagogical purposes, conditioned samplepaths are
 simulated in two steps: first, unconditioned samplepaths are simulated;
 second, conditioned samplepaths are obtained using conditioning by kriging.
 In practice, these two steps can be carried out all at once using
 stk_generate_samplepath (see, e.g., stk_example_kb09).

 See also: stk_generate_samplepaths, stk_conditioning, stk_example_kb09



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
 STK_EXAMPLE_KB05  Generation of conditioned sample paths



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb06


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 562
 STK_EXAMPLE_KB06  Ordinary kriging VS kriging with a linear trend

 The same dataset is analyzed using two variants of kriging.

 The left panel shows the result of ordinary kriging, in other words,  Gaussian
 process interpolation  assuming a constant (but unknown) mean. The right panel
 shows the result of adding a linear trend in the mean of the Gaussian process.

 The difference with the left plot is clear in extrapolation: the first predic-
 tor exhibits a  "mean reverting"  behaviour,  while the second one captures an
 increasing trend in the data.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
 STK_EXAMPLE_KB06  Ordinary kriging VS kriging with a linear trend



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb07


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 68
 STK_EXAMPLE_KB07  Simulation of sample paths from a Matern process



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 68
 STK_EXAMPLE_KB07  Simulation of sample paths from a Matern process




# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb08


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 323
 STK_EXAMPLE_KB05  Generation of conditioned sample paths made easy

 It has been demonstrated, in stk_exampke_kb05, how to generate conditioned
 sample paths using unconditioned sample paths and conditioning by kriging.

 This example shows how to do the same in a more concise way, letting STK
 take care of the details.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
 STK_EXAMPLE_KB05  Generation of conditioned sample paths made easy



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
stk_example_kb09


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 464
 STK_EXAMPLE_KB09  Generation of sample paths conditioned on noisy observations

 A Matern Gaussian process model is used, with constant but unknown mean
 (ordinary kriging) and known covariance parameters.

 Given noisy observations from the unknown function, a batch of conditioned
 sample paths is drawn using the "conditioning by kriging" technique
 (stk_generate_samplepaths function).

 See also: stk_generate_samplepaths, stk_conditioning, stk_example_kb05



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 79
 STK_EXAMPLE_KB09  Generation of sample paths conditioned on noisy observations





