[R-sig-Geo] question about regression kriging

[ONKELINX, Thierry]

Edzer,

One assumes a normal distribution of the predictions in every point when
calculating a confidence interval based on the kriged mean and variance.
AFAIK sequential Gaussian simulation doesn't have to yield normally
distributed predictions per point. Therefore can the confidence
intervals based on SGS differ from those based on the kriged mean and
variance. Or am I missing something?

Thierry


------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
methodology and quality assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium 
tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be 
www.inbo.be 

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey

-----Oorspronkelijk bericht-----
Van: Edzer Pebesma [mailto:edzer.pebesma at uni-muenster.de] 
Verzonden: woensdag 9 april 2008 10:57
Aan: ONKELINX, Thierry
CC: David Maxwell (Cefas); r-sig-geo at stat.math.ethz.ch
Onderwerp: Re: [R-sig-Geo] question about regression kriging

Thierry,

how would you setup a Gaussian simulation such that the end result is 
different from the case where these confidence intervals were directly 
computed from the kriged mean and variance and a Gaussian assumption on 
the errors?
--
Edzer


ONKELINX, Thierry wrote:
> Dear David,
>
> An other option would be to use sequential gaussian simulation. That
> will allow to calculate confidence intervals in the logit scale. These
> can be back-transformed into the original scale because the logit
> transformation is monotone. 
>
> HTH,
>
> Thierry
>
>
------------------------------------------------------------------------
> ----
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature
> and Forest
> Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
> methodology and quality assurance
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium 
> tel. + 32 54/436 185
> Thierry.Onkelinx at inbo.be 
> www.inbo.be 
>
> To call in the statistician after the experiment is done may be no
more
> than asking him to perform a post-mortem examination: he may be able
to
> say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
> The combination of some data and an aching desire for an answer does
not
> ensure that a reasonable answer can be extracted from a given body of
> data.
> ~ John Tukey
>
> -----Oorspronkelijk bericht-----
> Van: r-sig-geo-bounces at stat.math.ethz.ch
> [mailto:r-sig-geo-bounces at stat.math.ethz.ch] Namens Edzer Pebesma
> Verzonden: dinsdag 8 april 2008 20:50
> Aan: David Maxwell (Cefas)
> CC: r-sig-geo at stat.math.ethz.ch
> Onderwerp: Re: [R-sig-Geo] question about regression kriging
>
> David Maxwell (Cefas) wrote:
>   
>> Hi,
>>
>> Tom and Thierry, Thank you for your advice, the lecture notes are
very
>>     
> useful. We will try geoRglm but for now regression kriging using the
> working residuals gives sensible answers even though there are some
> issues with using working residuals, i.e. not Normally distributed,
> occasional very large values and inv.logit(prediction type="link" +
> working residual) doesn't quite give the observed values.
>   
>> Our final question about this is how to estimate standard errors for
>>     
> the regression kriging predictions of the binary variable?
>   
>> On the logit scale we are using
>>  rk prediction (s0) = glm prediction (s0) + kriged residual
prediction
>>     
> (s0) 
>   
>> for location s0
>>
>> Is assuming independence of the two components adequate?
>>  var rk(s0) ~= var glm prediction (s0) + var kriged residual
>>     
> prediction (s0) 
>   
>>   
>>     
> In principle, no. The extreme case is prediction at observation 
> locations, where the correlation is -1 so that the final prediction 
> variance becomes zero. I never got to looking how large the
correlation 
> is otherwise, but that shouldn't be hard to do in the linear case, as 
> you can get the first and second separately, and also the combined
using
>
> universal kriging.
>
> Another question: how do you transform this variance back to the 
> observation scale?
> --
> Edzer
>
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