Quantifying parameter uncertainty in a three-parameter model of speech and voice adaptation using early- and late-window pitch-shift responses

Sensorimotor adaptation within the Directions Into Velocities of Articulators (DIVA) framework (including DIVA, LaDIVA, and SimpleDIVA) is governed by auditory feedback, somatosensory feedback, and feedforward mechanisms. SimpleDIVA provides a reduced three-parameter formulation that enables direct estimation of auditory and somatosensory feedback control gains, as well as the learning rate of the feedforward command from trial-by-trial adaptation data; however, it provides point estimates without uncertainty information. This limitation becomes critical for subject-specific analyses based on noisy data. We introduce a probabilistic inference framework that estimates posterior distributions and quantifies how parameter uncertainty propagates to predicted trajectories. The method uses particle-based likelihood inference, sampling candidate parameter sets from prior distributions and weighting them according to their likelihood. We compare a late-window-only variant with a joint early–late formulation that treats early-window (feedforward-dominated) and late-window (feedback-engaged) responses as complementary observations. Monte Carlo simulations across eight measurement noise levels evaluate the coverage and width of credible intervals, as well as estimation error. Results show robust estimation of feedback gains under both formulations. The joint early-late approach improves learning-rate inference, yielding narrower intervals, reduced bias, and improved trajectory recovery while maintaining near-nominal coverage at empirically relevant noise levels.