Information-based learning, with thoughts on optimal experimental design.

The information approach to optimal experimental design
is widened to include information-based learning more
generally, drawing on the classical work of Renyi, Lindley,
de Groot and others. Learning is considered as occurring
when the posterior distribution of the quantity of interest
is more peaked than the prior, in a certain sense.

A key theorem states when this is expected to occur. Some
special examples are considered which show the boundary
between when learning occurs and when it does not.