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24,889 lactation productions with missing traits which were collected 19,807 cows from 1997 to Apr. 2000 for progeny test of dairy cattle in Korea by Dairy Cattle Improvement Center were used to estimate genetic parameters for milk production. A Gibbs sampling vs Bayesian inference was used in order to sample from marginal posterior distribution of (co)variance components and coupling chains as a kind of multiple sequences of chains were used to determine convergence to the stationary distribution. Using Gibbs sampling, genetic parameters could be estimated with more than 300,000 equations. The coupling chains with different random number seeds could not find convergence point. But using starting values as a good prior information for (co)variance components should be helpful to converge at fast. Genetic parameter estimates for lifetime lactation productions with repeatability model were a little bit lower than or similar to estimates which were used for national evaluation in US even though those of first lactation were as low as not reliable. Mean estimates of heritability in repeatability model were 0.28, 0.26, 0.24, and 0.25 for milk, fat, protein, and SNF, respectively. Mean estimates of genetic correlations in the same model were 0.51, 0.86. 0.73 for milk vs fat, milk vs protein, and fat vs protein, respectively. The fractions for permanent environmental variation of total variation at all lactation traits in this study were as low as about 10 % and means of repeatability were 0.38 for milk yields and 0.35 for fat, protein and SNF yields, respectively. When considering the small fractions of these variations, we presume that low correlation between lactation productions according to parity and multiple trait models would be recommended rather than a repeatability model.
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