Geoscience Reference
In-Depth Information
References
evaluate the impact on OIP. Plot this impact as
a tornado chart by ordering the input variables
in descending order of impact.
Question 5:
Consider now varying each input variable
(keep all other variables at the base case) by
changing its value by ± 5 % increments from
the base case value until say ± 20 %. For each
case evaluate the change in OIP, and plot this
as a spidergram.
Question 6:
Rather than changing each input variable by
a percentage difference from the base case,
change each input by a set of percentages.
For this, consider evaluating OIP as you
change an input variable based on its deciles.
Now plot this result in a similar format to a
spidergram, and comment on any differences
you notice from the spidergram in the previ-
ous question.
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12.5.2
Part Two: Loss Functions
The consequences of over and under estimation are often
not the same. The two common loss functions, however, are
symmetric.
Question 1:
Prove that the mean of a distribution always
minimizes the mean squared error loss func-
tion, that is, a loss function where the loss
increases as a square of the error for both over
and under estimation.
Question 2:
Prove that the median of a distribution always
minimizes the mean absolute error loss func-
tion, that is, a loss function where the loss
increases as the absolute value of the error for
both over and under estimation.
Question 3:
The L-optimal value is a speciic quantile of
the distribution of the penalty for over and
under estimation is both linear with different
slopes. The 0.5 quantile or median is optimal
if the slopes are the same. What is the quan-
tile for arbitrary (different) slopes for over and
under estimation?
