[R-sig-Geo] Kriging with uncertain data

[Edzer Pebesma]

If the only problem is to krige these data, the solution is pretty
trivial; add a location specific value to the nugget; this is what
Delhomme in 1978 coined as regression kriging [1] (kriging of regressed
rather than observed values, using estimates + estimation errors).

An implementation is found in gstat, look up argument "weights" in
?gstat; you can use this argument in gstat::krige

Trickier is to infer the variogram of the underlying, unobserved
stationary variable from your estimates + estimation errors, in
particular when these estimation errors are rather large and/or vary
strongly. Anyone knows a good ref to a paper that tackles that issue?


[1] Delhomme, J. P. "Kriging in the hydrosciences." Advances in water
resources 1.5 (1978): 251-266.

On 07/10/16 10:27, Santiago Beguería wrote:
> Dear Ákos,
> 
> I was referring to the former: I have data with two values at each location: measured value and uncertainty of the measurement. So, each observation is in fact a statistical variate, which we can assume is Gaussian distributed. Hence, my two values are the expected (mean) and the variance of the distribution.
> 
> Cheers,
> 
> Stg
> 
> 
>> El 7 oct 2016, a las 8:39, Bede-Fazekas Ákos <bfalevlist at gmail.com> escribió:
>>
>> Dear Santiago,
>>
>> you mean you have two values at each location (observed value and uncertainty)? Or you have an observed value that is the sum of the real value and the observation error (uncertainty). If the last, then I think using the gstat::krige() function is straightforward, since the result of the function contains the variance of the prediction ("Attributes columns contain prediction and
>> prediction variance"; https://cran.r-project.org/web/packages/gstat/gstat.pdf).
>>
>> HTH,
>> Ákos Bede-Fazekas
>> Hungarian Academy of Sciences
>>
>>
>>
>> 2016.10.06. 11:52 keltezéssel, Santiago Beguería írta:
>>> Dear R-sig-geo list members,
>>>
>>> I am curious about what are sensible approaches to spatial interpolation, most especially by using kriging, in the context of uncertain data.
>>>
>>> Suppose one has a dataset of values observed at different locations, and each value consists on the expected value and its variance. Variance here represents the uncertainty related to the observation, and shows spatial variation due to external factors, for instance the geological setting affecting the quality of the measurement.
>>>
>>> How would you proceed to model the spatial distribution of this variable, including propagation of the (spatially varying)?
>>>
>>> I suppose one approach could be by simulation, but at there other ways of propagating the uncertainty that do not involve potentially expensive (in computation time) simulation approaches?
>>>
>>> Cheers,
>>>
>>> Santiago Beguería
>>> CSIC
>>> Spain
>>>
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>>
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-- 
Edzer Pebesma
Institute for Geoinformatics  (ifgi),  University of Münster
Heisenbergstraße 2, 48149 Münster, Germany; +49 251 83 33081
Journal of Statistical Software:   http://www.jstatsoft.org/
Computers & Geosciences:   http://elsevier.com/locate/cageo/

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