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Heritability and genetic correlations for carcass traits in Korean cattle(Hanwoo) were estimated using REML algorithm and Bayesian inference via Gibbs sampling on age-constant basis and weight-constant basis and those estimates were compared between different models and different algorithms. Those parameter estimates with REML were similar to means and median for distribution of estimates in post-Gibbs analysis. For estimating those parameters using Gibbs sampling, 1500 estimates by each parameter were retained and used among 30,000 samples to avoid each two adjacent samples to be correlated after $quot;burn-in$quot; period of 2000 cycles were discarded. The little bit difference between estimates by REML and those by Gibbs sampling might be due to effective number of samples, so some more samples should be needed to get close to true values. Heritability estimates on weight-constant basis as that carcass weights were adjusted were little bit greater than age-constant basis as that age at slaughter were adjusted as covariate. This result indicated that genetic variation for carcass traits based on weight-constant might be larger than that based on age-constant so that for selecting bull for improving meat quality, breeding values based on weight-basis might be better than those based on age-constant basis. Heritability estimates for carcass traits from single trait analyses were similar with those from multiple trait analyses. The estimates of heritabilities were .21∼.22, .30∼35, .33∼.49, .31∼.38, and .34∼.40 for carcass weight, dressing percentage, longissimus muscle area, backfat depth and marbling score, respectively. Further study was needed for estimates of genetic parameters on marbling score using another methods like threshold model which is a kind of methodology on augmentation of non-observable variables under the normal distribution because the observations of marbling score seemed to be not normal distribution.
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