I'm certainly not a guru, but like you, need to understand these
concepts. I have also just started reading Ed's oxymoron paper. In my
early days of trying to understanding this, this is how I interpret the
1. Blocks estimated using OK give an average block grade. Typically,
there is some smoothing that has taken place. If you compare the average
of the all the blocks mined during a production period against what the
mill recovers for the same period (say a year) you should find very
little discrepancy - this is usually the case. This is the
"conditionally unbiased" factor.
2. What OK, does not do, is discriminate between the parts (eg. SMU) of
that estimated block that are above ore grade, and those parts below ore
grade. This is the realm of Uniform Conditioning or Indicator Kriging
(depending on what approach you want to take). The result of the
smoothed OK estimate is that some ore blocks are assigned to waste, and
some waste blocks are assigned to ore. This is the "accurate predictor"
If I am correct, Ed is saying that an OK estimate will give you a
conditionally unbiased estimate (on the block scale), but on the smaller
than block scale (SMU for example) it becomes difficult to accurately
distinguish between ore and waste grades, using OK.
I hope this is correct, but if not, then please correct me.
Maybe this topic has been done to death, but I'd like to poke the
carcass if I may...
Edward Isaaks via AI (15 February 2006) said of a paper by Van et al on
kriging neighbourhood analysis:
"..a paper...that actually proposes a method for designing the kriging
search neighborhood based on minimizing conditional bias. Horrifying -
do they not realize that such practice actually increases the estimation
error of the predicted tonnes and grade above cutoff? This paper is
probably the worst (best?) example I have seen of a faulty misconception
in 25 years of ore resource assessment. One can almost understand why
geostatistics might be labeled a scam."
This view is also shared by some of my colleagues and acquaintances, but
then on the other hand some consulting houses compute the statistics
outlined in this paper (slope of regression, weight of the SK mean etc)
and others such as "kriging efficiency" as a matter of course - are they
barking up the wrong tree or are these statistics helpful in certain
Ed also said "...in mining applications (where geostatistics has its
roots) conditional bias is actually irrelevant, unless the estimates are
used for grade control"
Can we, for the benefit of my embryonic but inquisitive geostatistical
mind, thrash out this topic - the pros and cons of conditional bias -
when is it good, when is it bad (ie: need to minimise it), how do you
quantify it, how does minimising conditional bias increase estimation
error, what is the importance of the search neighbourhood and sample
selection, means of determining the best size/orientation etc...and why
is there the apparent lack of unity of opinion on this issue?
Speak to me gurus!
Rio Tinto OTX
Phone: +61 7 3327 7676
Mobile: 0408 015 837
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