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stk_example_doe01


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 STK_EXAMPLE_DOE01  Examples of two-dimensional designs

 All designs are constructed on the hyper-rectangle BOX = [0; 2] x [0; 4].

 Examples of the following designs are shown:
  a) Regular grid                         --> stk_sampling_regulargrid,
  b) "Maximin" latin hypercube sample     --> stk_sampling_maximinlhs,
  c) RR2-scrambled Halton sequence        --> stk_sampling_halton_rr2,
  d) Uniformly distributed random sample  --> stk_sampling_randunif.



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 STK_EXAMPLE_DOE01  Examples of two-dimensional designs



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stk_example_doe02


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 STK_EXAMPLE_DOE02  "Sequential Maximin" design

 In this example, a two-dimensional space-filling design is progressively
 enriched with new points using a "sequential maximin" approach. More
 precisely, the k-th point X(k, :) is selected to maximize the distance to the
 set of all previously selected points X(1, :), X(2, :), ..., X(k-1, :).

 NOTES:

  * The resulting design is NOT optimal with respect to the maximin criterion
    (separation distance).

  * This procedure is not truly a *sequential* design procedure, since the
    choice of the k-th point X(k, :) does NOT depend on the response at the
    previously selected locations X(i, :), i < k.

 REFERENCE

  [1] Emmanuel Vazquez and Julien Bect, "Sequential search based on kriging:
      convergence analysis of some algorithms", In: ISI - 58th World
      Statistics Congress of the International Statistical Institute (ISI'11),
      Dublin, Ireland, August 21-26, 2011.



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 STK_EXAMPLE_DOE02  "Sequential Maximin" design



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stk_example_doe03


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 STK_EXAMPLE_DOE03  A simple illustration of 1D Bayesian optimization

 Our goal here is to optimize the one-dimensional function

    x |--> x * sin (x)

 over the interval [0; 4 * pi].

 A Matern 5/2 prior with known parameters is used.

 Evaluations points are chosen sequentially using the Expected Improvement (EI)
 criterion, starting from an initial design of N0 = 3 points.



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 STK_EXAMPLE_DOE03  A simple illustration of 1D Bayesian optimization





