(a) Cumulative distribution of ﹩{\chi }_{l=1g}^{2}﹩ values as a function of the mixing-length parameter α. (b) Cumulative distribution of ﹩{\chi }_{{\rm{a}}{\rm{l}}{\rm{l}}}^{2}﹩ values as a function of the mixing-length parameter α. The blue vertical lines indicate the probability-weighted mean values derived from the Bayesian marginal likelihood analysis, and the dashed line represents the median value. The red stepped line with filled circles represents the CDF. The gray bars represent the PDF.