Sensitivity analysis with clustered data
From: R.H. Allen (kkarie_at_hotmail.com)
Date: 01/13/05
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Date: Thu, 13 Jan 2005 11:16:02 -0500
Quite awhile back I posted a question on this topic, with no luck. My
post was complicated, but I think I've found a way to simply my query
and I'd like to give it another go.
Suppose I'm modeling a widget whose output can be represented by the
function f(_x_), where _x_ is a vector of input values. I do N
iterations of Monte Carlo simulation, randomly choosing _x_ at each
iteration. Next, I select P values of f and sum them; call the sum S.
(In practice, S is a little more complicated than a simple sum, but
summing works for illustrative purposes.)
What I would now like to know is the sensitivity of S to the elements of
_x_. Obviously, the problem is that I have P values of x_1, x_2, etc.
for every value of S.
One thought that has occurred to me is to take each cluster of P vectors
_x_, test the sensitivity of S with respect to the mean, variance, min,
max, etc. of each of the elements of _x_. It would mean a whole bunch of
sensitivity analyses instead of just one, but might produce exactly the
information I am after. My worry there is that the inputs _x_ represents
will become convolved with one another and that I will reach inaccurate
conclusions.
Any suggestions or insights greatly appreciated!
alan
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