Best interpolation methods

[Maya_MaryMathews]

How can one fix the different parameters in the  geostatistical analyst tool for various interpolation techniques? such as power for IDW, Smoothening parameters for RBF, range ,sill and nugget for kriging.
Is there any range for these parameters? Should trend, transformations necessary to be considered?

[EricKrause]

Most parameters apply only for that particular interpolator.  The Power in IDW, for example, has no analogous parameter in any other interpolators.

Global Polynomial Interpolation, Local Polynomial Interpolation, and Kernel Smoothing are all based on polynomials, so the Order of Polynomial means the same thing in each tool.  Additionally, LPI and KS share Kernel types because they're based on local kernels.

The only parameters that are shared across the board are related to the searching neighborhood (except when you introduce barriers).

The domain of each parameter depends on what the parameter does (for example, the range in kriging has to be greater than 0).  These domains are all documented, and if you try to use a value outside that domain, the software will throw an error telling you that it is outside the parameter domain.

You should always consider trend removal and transformations, but that doesn't mean you have to use them.  Only use them if they help create a better model (which you can judge with crossvalidation statistics).

[Maya_MaryMathews]

Thank you

I would like to know whether there is any specific range for RBF interpolations?
Because when i did my work, i obtained a default parameter as 30.262 for completely regularised spline, 43.588 for spline with tension and 1E20 for tension spline. Can i continue my work with these default parameters? Is this the right way?

To find the best interpolation methods, is it the way  that i change the parameters for one type of interpolation method and find the best model from it and again find best models for other methods by changing their corresponding parameters.

For my work , is it necessary to create test data and training data and then do the analysis to get the best model?

[EricKrause]

The default Kernel Parameter in RBF is calculated such that it minimizes the Root-Mean-Square error (RMS) during crossvalidation.  Comparing the RMS values from different models is the most common method of deciding which model is better.  Comparing crossvalidation statistics between models can get complicated, but the rule-of-thumb is to use the model with the lowest RMS. All interpolation methods will calculate RMS during crossvalidation, and it has the same meaning for all interpolators, so it can be compared across the board to decide which interpolation method (and which parameters) to use.

Theoretically, the kernel parameter can take any real number, but computer limitations keep the possible range between +/- 1.79769 x 10^308.

[Maya_MaryMathews]

Thank You So Much


While i did ESDA, with the temperature data , in the Histogram tool i observed that my data is not normally distributed and when i did transformations I couldnt  find any change. Why is it like that?
Was my data normally distributed? But it didnt show a bell shaped graph that appear for a normal distribution. I am attaching the  screen shots of histogram and QQ plot result please check and help me

[EricKrause]

From that Word doc, it doesn't look like a Log transformation is a good choice.  Instead, try a Normal Score Transformation. In the Geostatistical Wizard, use Kriging, then on the second page, use "Simple" as the kriging type.  The default transformation will be "Normal Score."  Click Next.  On this screen, change "Type" to Gaussian Kernels.  See if the default fit seems to fit your histogram.  You may need to try changing the number of kernels if the default fit doesn't look good.  If you find a transformation that fits your histogram, the software will automatically do the back-transformation for you, so the result of the kriging will be in the original units (not transformed units).

The Normal Score transformation is the most powerful and functional transformation, but it's only available for Simple, Probability, and Disjunctive kriging.

[Maya_MaryMathews]

Thank you

But if i want to any do any other kriging other than simple and disjunctive , can i assume the histogram data as normal as obtained  in the word-Will there be any wrong with this? Is this assumption correct?

[EricKrause]

The histogram and QQ plot look pretty good without a transformation; you'll probably be fine without one.  That being said, I would still try Simple Kriging with a Normal Score Transformation.

[Maya_MaryMathews]

Thank you so much for the reply

[Maya_MaryMathews]

What is the real difference between Completely regularized spline, spline with tension and thin plate spline?

How can we say that in RBF, the point Surface created must go through each measured sample value and also it predicts values above the maximum and below the minimum measured values