My background is not in statistics, but other engineering, so forgive my ignorance and lackof/misuse of terms. Let me paint a picture of my situation:

I have a large number of elements, each with its own probability contributing to the occurence of my "go or no-go" event. I'd liken it to having, say, thousands of dice, each with a different number of sides, and thus different probablities of rolling a particular number (like rolling a 1). The probability of rolling a particular number (for this argument's sake, rolling a 1), is not simply the probability of the dice with the lowest number of sides (essentially like flipping a coin, with a 1 and a 2 on it), but rather some mathematical combination of all the dice with all their varying number of sides.

The only problem is, I do not know the inherent probabilities (i.e. "number of sides") of each of my elements, or "dice". All I have is the outcomes of my simulations (go or no-go), my input variables (1 for each simulation) and now my observations of physical properties inside "the black box." I hope to now correlate the physical principles with the probability of an event occurring, however, as I said before, I do not know the inherent probabilities of each element in my "black box" contributing to an event's occurrence.

Let me put all the pieces together using a situation similar to Schroedingers Cat:

Say I have a box full of a bunch of different clear "orbs" (my elements). My simulation entails me shaking the box a certain amount (not so hard varying all the way to very hard; my variable input). After I shake it, the cat looks inside the box and either dies or doesn't die (go or no go). I do this 50 times and see that the harder I shake it, the more likely it is the cat dies, all without knowing what's going on in the box. (My old way of modelling the probability of event occurrence based on varying input).

However, now I take a look at what's going on in the box. The harder I shake the box, the more the orbs change color. And the harder I shake, the redder each orb gets. I notice that if the cat sees a certain level of redness in any 1 particular orb, it is more likely to die ("redness" being a tangible, quantitative value, that I would know).

The simplest way to do it is take the value of the "reddest" orb from each simulation of shaking and fit that to a probability distribution on whether that cat dies or not. However, the cat can see a certain level of "redness" at any of the orbs in the box, not just the

*most*red one, so this simple way is not the most accurate. The only problem is, I don't know how to obtain the inherent probabilities of each orb without first fitting a probability distribution. I want to model the probability of the event occurring based on all my elements, not just the one with the greatest value ("highest probability").

I'm not sure if this is a particular branch or theory in statistics, or if it's even at all clear what I'm trying to get at! But I would greatly appreciate if anyone can help me out or point me in the right direction to figure this out, I would greatly appreciate it. Please feel free to ask me any clarification questions!