## AI-GEOSTATS: Extreme bias in autocoviariance function estimator

Expand Messages
• Hi, I hope this is not a dumb question. I have set of sites which are discrete and connected by a graph. On each site (vertex in graph theory parlance) lives a
Message 1 of 3 , Dec 18, 2001
Hi,
I hope this is not a dumb question. I have set of sites which are discrete
and connected by a graph. On each site (vertex in graph theory
parlance) lives a population which is modeled as a discrete time ricker
model, n(t+1)=n(t)exp[r(1-n(t)/k) + e] - E + M, E is a proportion of the
population migrating out only along the edges of the graph and M is the
sum of migrants coming in for other vertices and e is a random error
term correlated in space but independent in time. Now I am interested in
the correlation cor(v_i, v_j) as a function of distance. I set the
migration to zero, so that after a sufficient amount of time all
populations hover around their equilibrium K. I have the correlation in
the random errors e specified as p^||s_i-s_j||, an isotropic covariance
that is a function of distance alone.

Now the question, if I calculate all pairwise correlations between
vertices and fit a smoother, I recover the specified corelation function
with very little bias (provided t is large enough), and this seems to work
for a relatively small sample of vertices. However if I caculate the
auto-correlation function using the standard estimators and average them
over time, or calculate the average of the standardized populations and
fit the auto-correlation function, the result is severely biased (under
estimates) the correlation as a function of distance, even for large v. I

Nicholas

CH3
|
N Nicholas Lewin-Koh
/ \ Dept of Statistics
N----C C==O Program in Ecology and Evolutionary Biology
|| || | Iowa State University
|| || | Ames, IA 50011
CH C N--CH3 http://www.public.iastate.edu/~nlewin
\ / \ / nlewin@...
N C
| || Currently
CH3 O Graphics Lab
School of Computing
National University of Singapore
The Real Part of Coffee kohnicho@...

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of any useful responses to your questions.
* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
* Support to the list is provided at http://www.ai-geostats.org
• Julhendra That is what your semi-variogram is for. Determine maximum distance and anisotropy (change with direction) from your experimental semi-variograms.
Message 2 of 3 , Dec 19, 2001
Julhendra

That is what your semi-variogram is for. Determine
maximum distance and anisotropy (change with

Your search strategy should also change with the shape
of your blast layout. Single blast patterns are
usually 'long and thin', meaning that a circular
search would be less than optimal. I don't know of any
papers which discuss this, but you can see our
strategy in the kriging game. This is freely

http://uk.geocities.com/drisobelclark/briefcase.html

and allows you to experiment with search patterns and
changes in semi-variogram model. It also allows you to
see the difference between kriging as a 'point'
estimation method (for mapping) and kriging an average
over a blast area. Unfortunately, this free package is
only 2d, but you may find it useful.

One other point you may find useful. In my experience,
working in 3d reduces to using the previous bench
blastholes. A full 3d approach is only useful if you
have good diamond or percussion drilling within the
search volume. If you are going to combine sampling
types, you need to determine whether the samples are
compatible or to use a co-kriging approach.

Isobel Clark

--- Julhendra Solin <Julhendra_Solin@...> wrote:
> Dear All,
>
> I am working on blasthole interpolation in open pit
> mine. Interpolation
> using ordinary kriging and grades interpolated also
> from above bench.
> Blasthole spacing about 10 m and bench height 15 m.
> Anybody could help me
> how to determine search distance and min/max of
> number of samples to krige
> the grade. May be some technical paper related to
> it.
>
> Thanks.
>
> Jul
>
>
> --
> * To post a message to the list, send it to
> ai-geostats@...
> * As a general service to the users, please remember
> to post a summary of any useful responses to your
> questions.
> * To unsubscribe, send an email to majordomo@...
> with no subject and "unsubscribe ai-geostats"
> followed by "end" on the next line in the message
> body. DO NOT SEND Subscribe/Unsubscribe requests to
> the list
> * Support to the list is provided at
http://www.ai-geostats.org

__________________________________________________
Do You Yahoo!?
Everything you'll ever need on one web page
from News and Sport to Email and Music Charts
http://uk.my.yahoo.com

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of any useful responses to your questions.
* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
* Support to the list is provided at http://www.ai-geostats.org
Your message has been successfully submitted and would be delivered to recipients shortly.