Post date: Feb 23, 2014 9:13:6 PM
M & S:
I may have some trouble in evaluating those differences for Mohamed. My gleaming armor is rusty, and the white horse is lame.
The bridge system's reliability function
R = ac + bd + ade + bce - abce - acde - abde - bcde - abcd + 2abcde
is easy to evaluate using our left-right trick because it is monotone in each variable.
But those differences that Mohamed wants to evaluate, e.g.,
Birnbaum(a) = R( |a=1) - R( |a=0) = c + de - bce - cde - bde - bcd + 2bcde
also has repeated variables after simplification. Unfortunately, it is NOT monotone in each of its variables, so our left-right trick won't work on it.
The function is constant for a of course, and monotone in both b and c (although negative for b). But it does not have constant sign for d or e. I suppose that means that we should focus on reducing repetitions of d and e, which suggests a strategy forward to find the Birnbaum differences, at least for this bridge problem. But of course this is little comfort to us generally because it means that our paper won't be able to claim that this approach will be very easy for other problems.
On the other hand, I don't think that this problem affects the "MORE TRIALS" approach to characterizing information gain that we discussed yesterday. Does it? I'll try to get that code to Mohamed today.
Scott
Hello Scott,
Well, that is an interesting fact, as it means that all results
relying on coherence are probably not directly extensible to
importance measure assessments.
As long as the structure function is small enough, I guess we can go
with a bazooka (even if it is to kill a mosquito) to have the answer.
Otherwise we would indeed get wide answers again... so for small
systems we can make an exact computation, yet for big systems this is
not so clear (but in those cases, perhaps the quick alternative may
gives us non-empty conclusions).
Information gain just use the monotone function, so my answer would be
no, it does not affect it.
Cheers
Sebastien