Geoscience Reference
In-Depth Information
Fig. 14.57
Conditional simulations, San Cristóbal, Bench 2,345
In grade control, the selection decision (which material
is ore and which is waste) has to be based on grade esti-
mates, z
*
(
u
). Since the true grade value at each location is
not known, an error can and will likely occur. The loss func-
tion
L
(
e
) attaches an economical value to each possible error.
The expected conditional loss can be found by applying a
loss function to a set of equi-probable simulated grade values
(conditional probability function) at each simulated node.
The minimum expected loss can then be found by simply
calculating the conditional expected loss for all possible val-
ues for the grade estimates, and retaining the estimate that
minimizes the expected loss. As described in Isaaks (
1990
),
in grade control the expected conditional loss is a step func-
tion whose value depends on the operating costs, and the
relative costs of miss-classification. This implies that the
expected conditional loss depends only on the
classification
of the estimate
z*
(
x
), not on the estimated value itself. For
example, the loss incurred when a block of leach ore is sent
to the mill is a function of the difference in processing costs
related to both leach and mill; it will, of course, also depend
on the
true block grade
, but not on the
estimated block grade
value itself.
Minimizing the loss in such a way can be related to mini-
mizing Type I (false positive) and Type II (false negative)
errors (Fig.
14.58
). In positively-skewed distributions, which
are characteristic of minerals of high intrinsic value, such
as precious and base metals, only a small proportion of the
rock mass is economic. This implies that it is not the same to
make a Type I (the material is thought to be ore, when it is
in fact waste) or a Type II error (the material is thought to be
waste, and in fact it is ore). The key difference in this method
is that the process does not necessarily minimize grade esti-
mation errors, but minimizes the economic consequences of
such errors.
