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--- analysis:cosmo2014:module4 [2014/08/13 18:34]
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-~~DISCUSSION~~
-===== Module 4 =====
-Goals:
-  * Construct some movement kernels for estimation of spatial priors
-  * Incorporate a dynamic spatial prior in your decoder
-==== Introduction ====
-In the previous module, we applied the decoder to each time bin independently, using a flat spatial prior. In effect, this assumes that the place representation can move around arbitrarily from one time step to the next. Clearly, however, a rat cannot move around arbitrarily but instead moves subject to smoothness and continuity constraints! We can use this domain knowledge to improve the performance of our decoder.
-Our approach will be similar to Kalman filtering, in that we can construct a model of the rat's movement. We can then use this model to generate a prediction of the rat's position $P(\hat{x}_t)|P(\hat{x}_{t-1})$. The hat is meant to indicate that these are all estimates since the decoder does not have access to the rat's true position $x$.