This study examines genetic breeding values and variance components of popping expansion and grain production by means of Bayesian inference and a mixed linear model approach in 96 S3 maize families. Best Linear Unbiased Predictors (BLUP) of family effect were obtained by considering the Restricted Maximum Likelihood (REML) method of variance component estimation. An Independence Chain algorithm (IC) was used as a method of Bayesian inference. Family and residual variance component values were very similar between the IC algorithm and the REML method. Heritability values showed imperceptible differences in the approximation between approaches. Differences in the standard deviation of these estimates were observed, with the REML approach clearly showing the largest result. Heritability of grain production was moderate to high for popping expansion, indicating that simple selection methods can be applied. Using an IC algorithm and the BLUP approach for breeding values, no important changes were seen infamily ranking, which was confirmed with high and significant Spearman’s correlations values (Γs) ranging from 0.9941±0.004 to 0.9973±0.001. Pearson’s correlation between the BLUP values of popping expansion and grain production was low, negative and insignificant (Γs=-0.0320%±0.02).We concluded that Bayesian inference via an IC algorithm could be an important tool to use in maize breeding like classical analysis using a mixed linear model procedure.