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This is very appropriate for the assignment, and reads very well.

Aside: It seems like the main reason for the hyperspherical space is that there can be a uniform prior (and so avoiding the bunching of the normal. Why not use a uniform on the unit cube? The main difference is that a hyperspherical space wraps around; is that actually exploited? (or Maybe hyperspherical is actually simpler than the cube, as there are no boundary conditions). Or is there something more fundamental?