OPTIMAL ADAPTIVE DESIGN OF EXPERIMENTS FOR STOCHASTIC DYNAMIC SYSTEMS
GILES HOOKER – CORNELL UNIVERSITY
This talk examines the design of stochastic experimental systems so as to best able to estimate parameters of the underlying dynamics. In systems ranging from ecology, neurobiology and economics, models of system dynamics can be paired with laboratory experiments to estimate parameters and gain insight into their underlying dynamics. When this is done, several experimental parameters can be chosen: the type and timing of observations, along with inputs.
In stochastic systems, maximal information is generally obtained from particular parts of state space and it is therefore advantageous to adapt inputs and observations 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.