Bayesian decision theory, the maximum local mass method, and color constancy

Bayesian analysis of the problem a b = 1.

Assuming uniform prior probabilities over the graphed region, (a) shows the posterior probability for gaussian observation noise of variance $0.18$. The noise broadens the geometric solution into a hyperbola--shaped ridge of maximum probability. (b) Note the different thickness of the ridge; some parts have more local probability mass than others, even though the entire ridge has a constant maximum height.

Modification Date:  October 21, 2011