[R-sig-Geo] Kriging with uncertain data

[Bede-Fazekas Ákos]

Dear Santiago,

in this case I would interpolate/krige the uncertainty as well. Since 
uncertainty might have different distribution, different covariates, and 
different spatial autocorrelation than those of the measured value, I 
would build a new kriging model (fit new semivariogram, etc.) and 
interpret the predicted values of krige() as the predicted measurement 
uncertainty. I'll have now two uncertainty maps: one is the 
interpolation uncertainty (variance from the result of the 
krige(measurement)) and the other is the interpolated measurement 
uncertainty (predicted values from the result of krige(uncertainty)). 
Afterwards, these two can be combined or can be used separately as well.

Have a nice day,
Ákos

2016.10.07. 10:27 keltezéssel, Santiago Beguería írta:
> 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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