Is there a way to force kriging to keep unchanged measured values of observation points?

For example: if the observed value of a location is 1, after the interpolation it could be 0.9 or even 0.5, depending on the other locations' values. I'd like to have 1 for that observed location after the prediction too.

I know that, considering the kriging formula, this is a stretch but predicting values where it is actually known seems to me a stretch as well. I found that the only prediction method that preserves observation points' values is IDW but this is not the best method to predict values for the other prediction locations.

I'm using R and the package "intamap".

I'm using the "automatic" method provided by "intamap" package. I need to use it for two reasons: the first is for the very strong skewness of my data and the second reason is that kriging interpolation is the final step of method I'm developing that is devoted to be user friendly for inexpert persons.

"Intamap" package claims to meet these two needs. The reason why I need to keep original data unchanged is that observation points represent the probability values of a phenomenon to occur. Pay attention, I'm not talking about indicator kriging, because observed values are just probabilities. So I need to provide inexpert users the geographical distribution of different degree of probabilities. If I have two observation points with 1 and 0.5 probability values, I need these values to be unchanged and that kriging interpolates the values in the prediction locations between them.

I hope to have been clear in my explanation. How can I proceed now?

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    How are you Kriging? If you are using some kind of automated "kriging" procedure you're probably out of luck. But if you can specify the variogram parameters, then there's a lot you can do. By forcing the nugget to zero and selecting a model that is relatively smooth at the origin, you can achieve your aims. But if such a model does not match the empirical variogram well, it's pointless to be kriging in the first place. What you really need to tell us is why you want the interpolated surface to honor the data and how you will be using that surface. – whuber Jun 24 '13 at 16:52
  • My reply is in the improved question – e-falcon Jun 24 '13 at 19:17
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    (1) Skewness does not indicate whether kriging is appropriate, but usually it indicates some preprocessing of the data is needed before doing any kriging, such as an initial nonlinear transformation. (2) Kriging is the opposite of user-friendly: complex, slow, and needing statistical analysis. (3) Kriging can on occasion predict values beyond the range of data. Presenting "probabilities" that are negative or greater than 1 could be a problem! (4) How exactly do you obtain data that are "probabilities"? Are these perhaps observed frequencies? There are crucial distinctions between the two. – whuber Jun 24 '13 at 19:23
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    There is a large literature on interpolation methods. Making a good choice depends on your application, on why you are interpolating, on the statistical nature of the data, and many more things. There is about a 25 year history now of papers that compare Kriging to alternative methods. Their results depend on the nature of the data and the skills of the analysts. An early paper in this area is Englund, EJ, A Variance of Geostatisticians: Math. Geo. 22:4 (1990), pp 417-455. – whuber Jun 24 '13 at 20:06
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    Possible duplicate of Is kriging an exact interpolation method? – Andre Silva Jan 4 '18 at 17:28

Kriging is an exact interpolator. You don't have to do anything. Check your settings if it is not.

from wikipedia

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    It is misleading to characterize kriging as "exact" because the surfaces it interpolates can be nondifferentiable and even discontinuous. When there is a nonzero nugget in the variogram, the interpolated surfaces will not look like your diagram. Instead, they will miss the original data points. If you plug in the precise coordinates of the original data points it will return the original values: basically, it leaps from its non-exact interpolated surface to the data points and right back again. That is not what is wanted here. – whuber Jun 24 '13 at 16:49
  • whuber: I disagree. Even with a nonzero nugget the surface will not miss the original points (in ordinary and simple kriging) – johanvdw Jun 24 '13 at 19:49
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    Johanvdw, You are not disagreeing with me, but you may be failing to appreciate what you are saying. Yes, kriging with a nonzero nugget "honors" the data. But it does so only by creating a discontinuous surface that jumps away from the interpolated values at the data points! In practice, the kriged surface is evaluated at the centers of a grid of points and none of those centers is exactly located at a data point. Thus, the interpolated surface that actually gets mapped fails to honor the data. – whuber Jun 24 '13 at 20:00
  • I still disagree: the surface will be smooth. – johanvdw Jun 24 '13 at 20:04
  • Assuming you mean the theoretical surface that does honor the data, I challenge you to prove it, then. The textbooks--as well as any test--will show you are wrong. If you mean the mapped surface, I have just explained why it appears smooth--but then it does not honor the data. – whuber Jun 24 '13 at 20:06

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