A number of important data analysis problems in neuroscience can be solved using state-space models. The optimal estimate of the state is its conditional expectation given the observation histories, but this expectation is computationally demanding when nonlinearities are present. Various authors have therefore used Gaussian approximations to posterior densities that appear in the formulation.
In the first part of the presentation, we investigate this approach, showing that the errors introduced by the approximation are not compounded across time. We then consider second-order expansions, and show that they can provide second-order accuracy in state estimates---but that no additional accuracy is possible by higher-order approximations. We discuss implementation of these methods and illustrate by decoding multielectrode motor cortical data.
In the second part of the presentation, we have developed real-time software which implements our decoding methods in conjunction with a brain-computer interface. We show results from a monkey using these methods to control a cursor on a computer screen, and compare the performance of our decoding methods to that of the population vector algorithm. We also discuss the difference between off-line and on-line analysis.