Fig. 4.

(A–C) Objective function as a function of the two parameters (stability and scale) for (A) the first (shifted) likelihood, (B) the second (unshifted) likelihood, and (C) the propagation kernel, while the respective other four parameters are held fixed. The gray shades represent the decimal logarithm of the objective function (effectively, logarithms of the negative log-likelihood), and lighter shades mean a better fit. Because of the logarithmic scaling, small changes in the shading represent large changes in the quality of the fit. The black crosses show the parameter values for the deepest local minimum in this range of parameters. Note that, even though the minimum in C is close to the Gaussian kernel (${\alpha }_{\mathrm{k}}=2$), a Gaussian kernel cannot fit the data well. Specifically, it cannot reproduce a non-Gaussian distribution of the baseline pitch, instead essentially matching the parabola in Fig. 2C.