Trace plot for a run of MCRC for 1000 cycles with 3 independent chains. The current values of all parameters were recorded every 10 cycles. Each color represents a different chain, and each panel represents a different dimension of each chain corresponding to a particular scalar parameter. The parameters are (top left) the mean intrinsic B − V color for HV SNe Ia, (top right) the mean intrinsic B − V color for NV SNe Ia, (bottom left) the residual standard deviation of the intrinsic B − V around the mean trend, and (bottom right) the average extinction of the exponential dust distribution. The chains converge rapidly to the posterior distribution, and the initial portions of each chain are discarded as "burn-in" before analysis.