[R-sig-Geo] question about regression kriging

[Edzer Pebesma]

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
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> say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
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>
> -----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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