1) Your formula for C_k^opt is wrong, see Eq 10: $C_k^opt = \frac{f’_k}{\sigma_k}\sqrt{\sigma_0^2+\epsilon}$.

2) You wrote that “If only x is used by the animal for decision making, but only y is recorded, then y will have choice correlations that are proportional to, but large than x.” Actually, I’d emphasize that this CAN happen, but does not ALWAYS happen. (I interpret your post as saying it always happens). Whether a non-decoded population has higher Choice Correlations or not depends on the specifics of the noise covariance. Interestingly, this strange circumstance does seem to hold for the regions we recorded.

Cheers,

-xaq

Thanks for the post! ]]>

Very informative post – “Integration dynamics and choice probabilities” ]]>

Ben

]]>