The calibration algorithm accurately computes the steady-state error covariance and convergence time as a function of learning rate for continuous signals.

<p>(A) The analytically-computed and the true error covariance and convergence time of the encoding model parameters (baseline, <b><i>η</i></b>_<i>x</i>, and <b><i>η</i></b>_<i>y</i> in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006168#pcbi.1006168.e002" target="_blank">(1)</a>) for different learning rates <i>s</i>, across a wide range of <i>s</i>. The top left panel shows the relation between the three quantities. The other three panels are projections of this plot to three planes, showing each of the three pair-wise relationships. All axes are in log scale. True quantities are computed from BMI simulations with periodic center-out-and-back training datasets. The analytically-computed values are obtained by the calibration algorithm according to Eqs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006168#pcbi.1006168.e022" target="_blank">(7)</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006168#pcbi.1006168.e024" target="_blank">(8)</a>. The analytically-computed and true values match tightly across a wide range of learning rates, showing that the calibration algorithm can accurately compute the learning rate for a desired trade-off between steady-state error and convergence time. (B) Adaptive estimation of the unknown observation noise variance using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006168#pcbi.1006168.e043" target="_blank">(11)</a> under different learning rates <i>s</i>. The bottom three panels are zoomed-in versions of the top panels to show the transient behavior of the estimated noise variance, which converges to its true value in all cases.