  The "mind-brain supervenience" conjecture suggests that all mental properties
are derived from the physical properties of the brain. To address the question
of whether the mind supervenes on the brain, we frame a supervenience
hypothesis in rigorous statistical terms. Specifically, we propose a modified
version of supervenience (called epsilon-supervenience) that is amenable to
experimental investigation and statistical analysis. To illustrate this
approach, we perform a thought experiment that illustrates how the
probabilistic theory of pattern recognition can be used to make a one-sided
determination of epsilon-supervenience. The physical property of the brain
employed in this analysis is the graph describing brain connectivity (i.e., the
brain-graph or connectome). epsilon-supervenience allows us to determine
whether a particular mental property can be inferred from one's connectome to
within any given positive misclassification rate, regardless of the
relationship between the two. This may provide motivation for
cross-disciplinary research between neuroscientists and statisticians.
