RE: AI-GEOSTATS: spatial weights

2007-02-20 Thread bob sandefur 
Cautionary notes on using Thiessen polygons (or polyhedra) for obtaining
geometrically unbiased weights for the mean.

Beware of holes bottomed in ore.  Particularly really high-grade ore.

Beware of really large search radii for the polygons or polyhedra.
Particularly polyhedra.

 

  _  

From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf
Of Digby Millikan
Sent: Monday, February 19, 2007 20:51
To: 'Bill Thayer'
Cc: AI Geostats mailing list
Subject: RE: AI-GEOSTATS: spatial weights

 

 You have to uncluster the data e.g. in resource exploration programs often
more sampling takes place 

in the higher grade zones, so this has to be compensated for by using an
equal amount of sample 

data from each area. If two samples are taken at one location it makes sense
to average them, and 

 if the data is normally distributed and stationariay the data within each
cell is normally distributed 

so the average of that cell, is the mean of the data within it?

 

  _  

From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf
Of Bill Thayer
Sent: Saturday, 17 February 2007 7:29 AM
To: ai-geostats@jrc.it
Subject: AI-GEOSTATS: spatial weights

 

In Isaaks and Srivastava's Applied Geostatistics (1989), the use of
'de-clustering' weights are described as a method for computing estimates of
the mean and variance with data that are clustered geographically.  

 

I would appreciate feedback regarding the theoretical basis for using
spatial weights to compute estimates of the mean and (population) variance,
and for making inferences regarding population parameters.  Through
simulation tests, I have some evidence that this method performs fairly well
with weights derived from Thiessen polygons for populations with varying
degrees of spatial autocorrelation and skewness.  However, I am not aware of
any theoretical basis/justification for the weights.  Intuitively, the use
of spatial weights to account for geographic location of the observations
(and possibly spatial autocorrelation among the observations) seems
analogous to the common practice in survey statistics of adjusting sample
weights to correct for non-response, etc, where the objective is to adjust
the weights to account for observed differences between some attribute of
the observations (e.g., socioeconomic status) and the target population.
In the spatial weighting case, the adjustment is to correct for observed
geographical clustering.  One notable difference is that in many cases, the
data that I work with was not collected using random sampling methods.

 

Your feedback would be appreciated.

 

Best regards,

Bill

AI-GEOSTATS: RE: spatial weights

2007-02-20 Thread Isobel Clark 
Yes, but the problem with averaging the data in the cell is that the average 
has a different standard deviation, depending on the layout of the sampling 
within each cell. 
   
  So, if you decluster by averaging each cell you can end up with a set of 
cells which all come from different distributions -- same mean but different 
variance. Not stationary at all! Better to select one sample from each cell.
   
  Isobel
  http://www.kriging.com

Digby Millikan <[EMAIL PROTECTED]> wrote:
v\:* {behavior:url(#default#VML);}  o\:* {behavior:url(#default#VML);}  
w\:* {behavior:url(#default#VML);}  .shape {behavior:url(#default#VML);}
 You have to uncluster the data e.g. in resource exploration programs 
often more sampling takes place 
  in the higher grade zones, so this has to be compensated for by using an 
equal amount of sample 
  data from each area. If two samples are taken at one location it makes sense 
to average them, and 
   if the data is normally distributed and stationariay the data within each 
cell is normally distributed 
  so the average of that cell, is the mean of the data within it?
   
  
-
  
  From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Bill Thayer
Sent: Saturday, 17 February 2007 7:29 AM
To: ai-geostats@jrc.it
Subject: AI-GEOSTATS: spatial weights

   
  In Isaaks and Srivastava’s Applied Geostatistics (1989), the use of 
‘de-clustering’ weights are described as a method for computing estimates of 
the mean and variance with data that are clustered geographically.  
   
  I would appreciate feedback regarding the theoretical basis for using spatial 
weights to compute estimates of the mean and (population) variance, and for 
making inferences regarding population parameters.  Through simulation tests, I 
have some evidence that this method performs fairly well with weights derived 
from Thiessen polygons for populations with varying degrees of spatial 
autocorrelation and skewness.  However, I am not aware of any theoretical 
basis/justification for the weights.  Intuitively, the use of spatial weights 
to account for geographic location of the observations (and possibly spatial 
autocorrelation among the observations) seems analogous to the common practice 
in survey statistics of adjusting sample weights to correct for non-response, 
etc, where the objective is to adjust the weights to account for observed 
differences between some attribute of the observations (e.g., socioeconomic 
status) and the target population.   In the spatial weighting case,
 the adjustment is to correct for observed geographical clustering.  One 
notable difference is that in many cases, the data that I work with was not 
collected using random sampling methods.
   
  Your feedback would be appreciated.
   
  Best regards,
  Bill