Figure 2.

Model results. (A) Updated MLE model accounting for limb movement and sensory delays. If the limb moves with speed, $\mathrm{\nu }$, at time, $t$, we have delayed visual (${\mathrm{\mu }}_{\mathrm{\tau }\mathrm{v}}$, red dashed line) and proprioceptive (${\mathrm{\mu }}_{\mathrm{\tau }\mathrm{p}}$, blue dashed line) feedback of the limb from sometime in the past instead of at its current position (red and blue solid lines). This leads to an erroneous bimodal state estimate (${\mathrm{\mu }}_{\mathrm{B}}$, purple dashed line) that is offset from the ideal bimodal estimate ($\widehat{{\mu }_B}$, purple solid line) by some error (purple arrow). (B) Simulation results suggest that as movement speed ($\mathrm{\nu }$) increases, the probability of obtaining an accurate bimodal sensory estimate decreases; in such cases, it may be better to use a unimodal state estimate. However, this also depends on the relative uncertainties of the two sensory modalities (top panel) and the relative time delay between the two modalities (bottom panel). (C) Observed data from Experiment 1 was used to estimate the bimodal variance via the MLE combination of the observed unimodal sensory variances. For the static estimation task (left), no relationship was observed between the bimodal variance and the observed bias. In contrast, in the dynamic estimation task (right) there was a clear correlation across individuals. Consistent with the model, this suggests that individuals with greater bimodal variance in the dynamic estimation task likely relied on an integrated state estimate and were more susceptible to discrepant information from the other sensory modality.