From spike rates to simple decisions: stochastic ODEs

11:30 room 430 Fishbach Bldg.

12 March, 2009

Prof. Philip Holmes

Department of Mechanical and Aerospace Engineering,
Program in Applied Mathematics, and Neuroscience Institute,
Princeton University


March 12, 11:30, Fishbach 430



I will describe how simple stochastic ODEs -- drift-diffusion processes --
derived as continuum limits of the sequential probability ratio test (SPRT),
can be used to describe evidence accumulation and decision-making in
the brain. The ODEs can be derived from biophysically-detailed models
of spiking neurons, and moreover, drawing on SPRT theory, they are
optimal in the sense that they deliver decisions of specified
accuracy in the shortest possible time, or the most accurate decisions
possible in a pre-specified time. But in real life, or in doing exams,
how should we balance accuracy and speed? In the first part of the talk
I derive an optimal speed-accuracy tradeoff for a very simple perceptual
decision task, compare human performance with this benchmark, and
discuss possible reasons for prevalent suboptimality, appealing to
information-gap theory. In the second part I address the incorporation
of prior information such as expectation of rewards, ending by showing
that two small rhesus monkeys can average 99% on their exams.
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