Kriging predictor

UQ with UQLab Community Q&A and How To
1

I have a question on how the kriging meta model plot is made. For instance, example 1 in the kriging manual has figure 8 which is a result kriging predictions and the inputs.

My question is how does one come up with the plot and what is the governing equation behind uq_display based on the beta and sigma^2 obtained from uq_print.

I can not seem to find the uq_display code and the equations used to obtain the plot figure 8.

Any clarification will be greatly appreciated !

1 Like
2

Hi @mercya,

Welcome to UQWorld :smile: !

Figure 8 is based on Kriging predictor of Eqs. (1.6) and (1.7) in the Kriging User Manual. The plot represents Gaussian random variables at some input points (\mathbf{x}) conditioned on the observed data (the black filled circles you see in the plot). To compute both equations, it is assumed that we already know everything about the Kriging model[1]:

  • the trend basis functions (\mathbf{f})
  • the corresponding coefficients of the trend function \mathbf{\beta}
  • the correlation function R
  • the corresponding parameters of the correlation function (\mathbf{\theta})
  • the process variance \sigma^2
  • the observed points \mathcal{X} and \mathcal{Y}

Referring to Figure 8, the solid blue line and shaded gray area represent the mean of the Kriging predictor (Eq. (1.6)) and twice (well, 1.96) the standard deviation around the mean (Eq. (1.7)), respectively. It is plotted for 500 uniformly spaced points in the domain of the input. I think what’s displayed on uq_print should be enough to reproduce the plot.

uq_display function is an entry point for all the default display functions of UQLab objects (MODEL, ANALYSIS, INPUT). In the case of Kriging MODEL object, uq_display function actually runs uq_Kriging_display.

I hope this answers your question.

  1. If we don’t, then it becomes an estimation problem for some of these parameters. ↩︎

2 Likes
3

Thank you @damarginal !

4

You’re welcome :smiley:!