Abstract: This talk considers the problem of designing inputs into stochastic experimental systems so that the resulting observations will yield maximal information about parameters of interest. In stochastic systems, maximal information is generally obtained from particular parts of state space and it is therefore advantageous to adapt inputs in response to the system's current state.
We demonstrate that in diffusion processes, the problem of adaptively maximizing Fisher information can be solved through control theoretic techniques and we demonstrate the numerical implementation of these. When only partial and noisy observations of a system are available, we consider imputing the system's state via a filter before applying the optimal policy as described above. Alternatively, maximizing Fisher Information for the partially observed system yields a non-standard control problem and we demonstrate an approximate solution in the context of discrete hidden Markov models.
The approaches described here have applications to numerous experimental systems; we demonstrate the efficacy of input design for parameter estimation through examples in ecology, single neuron experiments and experimental economics.