Some of us just don't know what they are or how to use them. I guarantee I'll be forming another study group some time in the future on the other topics you mentioned if they are as broad in application as you say. :)
My advice would just be to take a few stats courses. Make sure you're comfortable with your linear algebra inside out. Learn as many numerical methods as possible etc. etc.
In my mind, neural networks should only be used when you're trying to model actual biological systems. Otherwise, one should always use a proper model - since it actually gives insight into what's going on with the system, instead of just being a magic black box. Of course, notice that all commonly used ANN topologies have nothing to do with biology - feed forward, hopfield nets, kohonen maps etc. They have barely any resemblance to how actual neurons behave. Basically, they are just heuristics with a cool sounding name.
In my mind, neural networks should only be used when you're trying to model actual biological systems. Otherwise, one should always use a proper model - since it actually gives insight into what's going on with the system, instead of just being a magic black box. Of course, notice that all commonly used ANN topologies have nothing to do with biology - feed forward, hopfield nets, kohonen maps etc. They have barely any resemblance to how actual neurons behave. Basically, they are just heuristics with a cool sounding name.