[R-sig-Geo] question about regression kriging

[Edzer Pebesma]

Thierry, this is one of the frequent misconceptions in geostatistics.

Sequential Gaussian simulation yields for each point a normal 
distribution, with mean and standard deviation equal (in the limit of 
very many simulations) to the kriged mean and standard deviation.
--
Edzer

ONKELINX, Thierry wrote:
> 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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>> R-sig-Geo at stat.math.ethz.ch
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>>   
>>     
>
>