Fig. 3.

Relative biases of coincidence rate estimates from traditional and ensemble sorting, (T_⊥ - θ)/θ (black) and (gray), as functions of (A) the spike misclassification rate due to overlapping waveform clusters, (B) the coupling strength β, (C) the spike rate λ_A, and (D) the rate ratio λ_B/λ_A. The x axes of B and D are on a logarithmic scale. In each panel, parameters held constant are μ = 2 (17.3% misclassified spikes), λ_A = 4 Hz, λ_B/λ_A = 3, and β = 2. Ensemble sorting (gray) always yields unbiased estimates. Traditional sorting (black) never does, except when cells are independent and have equal rates (Theorem 1.1), or when waveform clusters are fully separated (Theorem 1.1 and Fig. 3A, zero error rate). Otherwise, the bias of T_⊥ increases as the waveform clusters overlap (Fig. 3A), the coupling strength increases (Fig. 3B), and the firing rates differ (Fig. 3D).