Discrete Prob_Noisy-And Distribution

Noisy-And Distribution

(DM prob. dist. for equations)

Usage:	NoisyAndDist (e, inh, b1, p1, ... bn, pn)
Definition:	P(e) = (1-inh) product i=1 to n (bi ? 1 : (1-pi))
Required:	0 ⋜ inh ⋜ 1 e, bi Boolean 0 ⋜ pi ⋜ 1

Use this distribution when there are several possible requirements for an event, and each has a probability that it will actually be necessary. Each of the necessary requirements must pass for the event to occur. Even then, there is a probability (given by inh) that the event may not occur (make inh zero to eliminate this).

Each bi is a boolean variable, which when true, indicates a requirement passed. e is also a boolean, which indicates whether the event occurs. Each of the pi are the probability that bi will be required to cause e.

If inh is zero, and only one possible requirement is false, say bk, then the probability for e is 1-pk. If more possible requirements are false, the probability will be lower. And if inh is nonzero, the probability will be lower. Reducing a pi always results in the same or higher P(e).

pi can be considered the “strength” of the relation between e and bi, with zero indicating independence (link could be removed), and 1 indicating maximum effect.