Variance and efficiency of the maximum likelihood decoder and its dependence on encoded angle and neural noise. (A) Variance in the estimates of the ML decoder (solid curve) depends nonmonotonically on the encoded angle. Dashed curve: the Cramèr-Rao bound with the bias taken into account; no estimator can achieve a lower variance. (B) Variance in the estimates of the ML decoder (solid curve) as a function of the neural noise comparing large and small encoded angles. At small angles, the strong bias alters the expected square dependence on noise into linear behavior. Dashed curves correspond to the Cramèr-Rao bound with the bias taken into account.