Before revision:  We note that experiments of the type considered are unable to distinguish between parametrized response functions lying along certain "diffeomorphic modes" in parameter space . We show how to derive these diffeomorphic modes and observe, fortunately, that such modes typically span a very low-dimensional subspace of parameter space. Therefore, given sufficient data, maximizing mutual information can pinpoint nearly all response function parameters without requiring any model of experimental noise .
After revision:  We note that experiments of the type considered are unable to distinguish between parametrized response functions lying along certain "diffeomorphic modes" in parameter space unconstrained. We term these directions "diffeomorphic modes" and present an equation that allows these modes to be derived systematically. The presence of diffeomorphic modes reflects a fundamental and nontrivial substructure within parameter space, one that is obscured by standard likelihood-based inference .