Say we have random variables A, B and C which are standard normals. They are also all independent. Now let's say we have D_1 = A+B and D_2 = (2A)+C. Now just for fun - if you like - let us say that we observe values for D_1 = -1 and for D_2 = 1. I was under the impression, that in this case, the MAP estimate for A must be 1/5, which is wrong. Then I thought, it could be zero, which is also wrong. Now I think, it could be 1/6, but I'm not sure