Hi all,

I am currently working on a problem that involves a lot of statistics and probability. Unfortunately I have limit expertise in both these areas and am wondering if anyone might be able to point me in the right direction of formula I should research/any programs that might do this already for me.
The issue is that I have an equation that is massive, between 10,000 and 1,000,000 input variables. Itís basically a black box that you through these inputs into and you get an answer. I cannot interrogate the actual equation.
What I want to achieve is two things:
find the variables that impact the answer the most.
Find an approximate answer for changing a variable based on a couple of runs of the equation.
Naturally by means of brute force, I could run the calculation millions of times and then determine the important inputs, but I donít have the time to do this.
Could also use nearest neighbour to determine what the answer would be a certain inputs, but this also would need a number of runs of the equation that would be too high.
Multi-dimensional interpolation analysis and genetic algorithms is what I have been looking at, but have not really found anything that satisfies me/I understand fully.
Would anyone happen to know a good book/papers/programs I could use that might preform this analysis?
Really massively stuck.
Thanks in advance.