Extended Data Fig. 4: Balance of errors is robust to changes in volatility.

a, As volatility increases, the posterior is faster to update and the error faster to decay (shown for the naively-adaptive code in response to an increase in variance). b-d, Biased codes produce qualitatively consistent patterns of performance regardless of volatility (upper panels), but the relative impact of biasing the code increases as volatility increases (lower panels). Higher volatility leads to relatively longer periods of mismatch (b, upper), higher mismatched errors and lower matched errors (c, upper), and higher global errors (d, upper). The percent change in each of these errors (measured relative to the naively-adaptive code and scaled by the difference in error between the static and oracle codes) increases as volatility increases (lower row), and the global error is thus minimized for larger values of bias (c-d; circled markers in upper panels).