Statistical, Stochastic, and Dynamical Models of Neural Decision Making
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Models of decision making provide a direct link between behavior and neurobiology. How does the encoding and accumulation of evidence by neural circuits impact decision making performance? Through data-driven and biophysically-based modeling, abstract models for simple decisions can be made more realistic, and may eventually explain how biological organisms can robustly make more complicated decisions. This dissertation investigates several models of this type, spanning a wide range of model abstraction. Deriving, parameterizing, and analyzing these models requires techniques from signal processing, mathematical statistics, stochastic processes, and dynamical systems. In many cases, we have found surprising roles for nonlinearities in the circuits that accumulate sensory evidence. In simple models, linear integration of evidence-encoding stimuli enables optimal decision making. This integration may be unstable in practice, however a nonlinear thresholding mechanism can ameliorate this deficit while retaining nearly optimal performance. Moreover, when sensory evidence is encoded in a correlated population of spiking neurons, preprocessing nonlinearities are exactly the prescription for optimal inference. We also examine a reduced model of a network of spiking neurons, in order to determine how nonlinear dynamics and noise combine to dictate performance. Our results suggest nonlinear dynamics may not significantly diminish performance, compared to the noise sources in biophysically motivated models of evidence accumulation. Combined with experimental studies, the exciting, and sometimes counterintuitive, effects of nonlinear computations may eventually elucidate the neural mechanisms of decision making.
- Applied mathematics