Abstract
Inverse problems are familiar occurrences, two examples of which occur when we are trying to hear interesting gossip amidst the din of a raging party or when we are trying to determine the location of neural activity in the auditory regions of a subject listening to music. In these problems the solutions are not unique; we may misunderstand what was being said or we may find neural activity in the wrong area of the brain, either way we are in a difficult situation. I will discuss deductive reasoning and plausible reasoning and show that deductive reasoning cannot be used in these difficult cases. This will lead to a Bayesian formulation of probability where we will learn to use plausible reasoning to infer the most probable solutions to our inverse problems. This technique will be demonstrated on the problem of sound separation and I will discuss how this may provide us not only with insight into how we ourselves perceive sounds, but also how we can infer neural source behavior and location.