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stk_example_kb01


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 STK_EXAMPLE_KB01  Ordinary kriging in 1D, with noiseless data

 This example shows how to compute ordinary kriging predictions on a
 one-dimensional noiseless dataset.

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

 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).

 Note that the kriging predictor, which is the posterior mean of the GP,
 interpolates the data in this noiseless example.

 See also: stk_example_kb01n, stk_example_kb02



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 STK_EXAMPLE_KB01  Ordinary kriging in 1D, with noiseless data



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stk_example_kb01n


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 STK_EXAMPLE_KB01N  Ordinary kriging in 1D, with noisy data

 This example shows how to compute ordinary kriging predictions on a
 one-dimensional noisy dataset.

 The Gaussian Process (GP) prior is the same as in stk_example_kb01.

 The observation noise is Gaussian and homoscedastic (constant variance).
 Its variance is assumed to be known.

 Note that the kriging predictor, which is the posterior mean of the GP,
 does NOT interpolate the data in this noisy example.

 See also: stk_example_kb01, stk_example_kb02n



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 STK_EXAMPLE_KB01N  Ordinary kriging in 1D, with noisy data



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stk_example_kb02


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 STK_EXAMPLE_KB02  Ordinary kriging in 1D with parameter estimation

 This example shows how to estimate covariance parameters and compute
 ordinary kriging predictions on a one-dimensional noiseless dataset.

 The model and data are the same as in stk_example_kb01, but this time the
 parameters of the covariance function are estimated using the Restricted
 Maximum Likelihood (ReML) method.

 See also: stk_example_kb01, stk_example_kb02n



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 STK_EXAMPLE_KB02  Ordinary kriging in 1D with parameter estimation



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stk_example_kb02n


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 STK_EXAMPLE_KB02N  Noisy ordinary kriging in 1D with parameter estimation

 This example shows how to estimate covariance parameters and compute
 ordinary kriging predictions on a one-dimensional noisy dataset.

 The model and data are the same as in stk_example_kb02, but this time the
 parameters of the covariance function and the variance of the noise are
 jointly estimated using the Restricted Maximum Likelihood (ReML) method.

 See also: stk_example_kb01n, stk_example_kb02



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 STK_EXAMPLE_KB02N  Noisy ordinary kriging in 1D with parameter estimation



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stk_example_kb03


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 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.lm property.

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



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 STK_EXAMPLE_KB03  Ordinary kriging in 2D



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stk_example_kb04


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 STK_EXAMPLE_KB04  Estimating the variance of the noise

 This example no longer exists.  See stk_example_kb02n instead.

 See also: stk_example_kb01n, stk_example_kb02n



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 STK_EXAMPLE_KB04  Estimating the variance of the noise



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stk_example_kb05


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 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



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 STK_EXAMPLE_KB05  Generation of conditioned sample paths



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stk_example_kb06


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 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.



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 STK_EXAMPLE_KB06  Ordinary kriging VS kriging with a linear trend



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stk_example_kb07


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 STK_EXAMPLE_KB07  Simulation of sample paths from a Matern process



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 STK_EXAMPLE_KB07  Simulation of sample paths from a Matern process




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stk_example_kb08


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 STK_EXAMPLE_KB08  Generation of conditioned sample paths made easy

 It has been demonstrated, in stk_example_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.



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 STK_EXAMPLE_KB08  Generation of conditioned sample paths made easy



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stk_example_kb09


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 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



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 STK_EXAMPLE_KB09  Generation of sample paths conditioned on noisy observations



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stk_example_kb10


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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



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 STK_EXAMPLE_KB10  Leave-one-out (LOO) cross validation





