Information-theoretic design of
experiments
Published as
Advances in Neural Information Processing 16
We discuss an idea for collecting data in a relatively efficient
manner. Our point of view is Bayesian and information-theoretic: on
any given trial, we want to adaptively choose the input in such a way
that the mutual information between the (unknown) state of the system
and the (stochastic) output is maximal, given any prior information
(including data collected on any previous trials). We prove a theorem
that quantifies the effectiveness of this strategy and give a few
illustrative examples comparing the performance of this adaptive
technique to that of the more usual nonadaptive experimental design. For
example, we are able to explicitly calculate the asymptotic relative
efficiency of the ``staircase method'' widely employed in
psychophysics research, and to demonstrate the dependence of this
efficiency on the form of the ``psychometric function'' underlying the
output responses.
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