Dear Dan and dear lists members,
I'm trying to explain my problem in two steps: the first is the theory, the
second one the practical application on my case study.

1)
Actually my errors are not so gaussian, however I think I could consider
them gaussian like.
It seems I've to set not zero the values of diagonal covariance matrix (used
for the variogram). Maybe I've to put in these matrix the measurements
errors instead zero. However, these are not actual variances, but ranges
deriving from the instrumental error. Is it possible to assume it as
confidence interval and use it such as the diagonal of covariance matrix?
This in theory.

But in practice???

2)
In practice, since I'm not a programmer, I've tried to use the psgp R
package in order to perform the interpolation of my variable with the
associated errors.
I've tried to use the Intamap on line service, but I've got some problem
with the net traffic (maybe) and I did not achieve the result.
So, I installed psgp and intamap in my computer, in order to perform the
calculation locally in my machine.

First ten rows of my dataset are as follows (names of variables:X, Y,
V2_PPM, ERR_V2_PPM:)

715946.900,4826440.340,2.280,0.140
722818.590,4824910.500,2.820,0.140
725514.920,4815239.460,2.380,0.130
722793.930,4810022.240,3.160,0.150
717682.540,4811456.540,3.040,0.140
712376.620,4806677.870,2.730,0.150
716270.140,4801958.660,2.650,0.140
721068.720,4801447.860,2.990,0.150
718812.980,4792920.780,4.450,0.170
722315.960,4788258.960,2.190,0.130
...

Actually I'm not uderstanding how process these data to interpolate my
variable V2_PPM.
The EPSG code il 23032.
Then, I think I've to set up my object as Intamap object  as follows (is it
correct?):

library(psgp)
coordinates(rock) = ~X+Y
data(grid.enrico)
gridded(grid.enrico) = ~x+y
proj4string(rock) = CRS("+init=epsg:23032")
proj4string(grid.enrico) = CRS("+init=epsg:23032")
# set up intamap object:
obj = createIntamapObject(
        observations = meuse,
        predictionLocations = grid.enrico,
        targetCRS = "+init=epsg:23032",
        class = "psgp"


However, I did not understand where I can declare the variable containing
the measurement errors.

Moreover, I do not understand how prosecute the process (i.e. experimental
variogram, variogram modelling, and finally kriging)

Could you give me some hint?

Thanks a lot in advance.


Enrico




2009/9/28 Cornford, Dan <D.Cornford@aston.ac.uk>

>  Enrico,
>
>
>
>   we have built an online system to perform this as part of the INTAMAP
> project – you can try this here:
>
>
>
> http://intamap.geo.uu.nl/~jon/intamap/tryIntamapj.php<http://intamap.geo.uu.nl/%7Ejon/intamap/tryIntamapj.php>
>
>
>
> If you paste in observations with Gaussian errors (I assume the +/- means
> one or two standard deviations – I would check this!) in the form x, y,
> value, stddev then our interpolation method (called psgp, which will shortly
> be released as an R and C++ library too) will provide a prediction of the
> mean and variance using a maximum likelihood Gaussian process method.
>
>
>
> The interface on that web page should allow you to try out the system very
> simply and the associated web site has details for more interactive ways of
> using the service, or installing the system on your own machine.
>
>
>
> If you want to have a quick look I suggest using the OMI NO2 data set which
> contains error estimates (this could take a little bit of time depending on
> the usage of the service!). Note the visualisation is still a little beta,
> so I would not entirely trust the legends!
>
>
>
> Further details will be added to the web site in the next few weeks!
>
>
>
> cheers
>
>
>
> Dan
>
>
>
> -------------------------------------------
>
> Dr Dan Cornford
>
> Senior Lecturer, Computer Science and NCRG
>
> Aston University, Birmingham B4 7ET
>
>
>
> www: http://wiki.aston.ac.uk/DanCornford/
>
>
>
> tel: +44 (0)121 204 3451
>
> mob: 07766344953
>
> -------------------------------------------
>   ------------------------------
>
> *From:* owner-ai-geostats@jrc.it [mailto:owner-ai-geostats@jrc.it] *On
> Behalf Of *Enrico Guastaldi
> *Sent:* 28 September 2009 13:55
> *To:* ai-geostats@jrc.it
> *Subject:* AI-GEOSTATS: Interpolation of measures with measurement errors
>
>
>
> Dear list members,
> I'm looking for some kind of interpolation for values of an environmental
> variable which has been measured together the measurement errors, for
> instance a measure is 45ppm +or- 10.7ppm, another one is 10ppm +or- 3ppm,
> and so on. In practice, measures and measurement errors are two independent
> variable.
> I could use some kind of kriging, however I exactly know the magnitude of
> each error at every sampled location, i.e. the value plus or minus the error
> gave me by the laboratory.
> Could anyone tell me what kind of function should I use for handling this
> problem?
> It should be nice some R package, of course, but I need to understand the
> background theory.
> Thanks in advance,
> Regards,
>
> Enrico Guastaldi
>

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