Signed Evidence Streams

Constructed streams

The target Σ is projected to the contrast space and eigendecomposed, Σ_c = Σ q_r w_rw_rᵀ. Each direction becomes a pair of Poisson streams with loadings ±w_r, base rate u_r = q_r/2λ₀, and drift split d_r = w_rᵀv. Bars show the loading of each alternative on each stream.

Sample trial — evidence trajectories

One complete trial of the compound-Poisson race: the shared stream lifts all counters by +1; each signed stream adds its loading vector. First counter to θ wins. Faded paths are the previous trial.

Choice probabilities vs threshold — convergence to the target MNP

Monte-Carlo choice shares at each θ (points ± 95% CI) against the target Multinomial-Probit probabilities computed from (v, Σ) directly (dashed asymptotes).

Recovered choice-relevant covariance

Left: target Σ_c = PΣP. Right: empirical λ₀²·P Ĉov(Z) P from counter fluctuations Z_i = (X_i(t_θ) − θ)/√θ at the current θ. As θ grows the race reproduces the target exactly.