(A) Basic encoding-decoding setup. The stimulus consists of two overlapping moving random dot patterns. A population of neurons codes for the two simultaneous stimuli. The task is to estimate the stimulus parameters—here the motion directions $s^1$ and $s^2$—from the noisy population response. (B) Maximum likelihood estimates across a number of trials. For a wide opening angle $s=(-0.2,0.2)$⁠, the distribution of estimates follows approximately a 2D gaussian distribution. True stimulus (red plus) and average estimate (green X) overlap. (C) For narrow opening angles, $s=(-0.02,0.02)$⁠, the distribution of estimates falls into two roughly equal parts: a gaussian-shaped distribution and a distribution along the line $s^1=s^2$⁠. True stimulus and average estimate now diverge (i.e., the estimate is biased). The sum and difference angles are indicated by $η$ and $θ$⁠, respectively. (All angles are in radians.)