Estimates of posterior distributions of genetic and phenotypic parameters and functions of them for individual test day milk yield are obtained for 28 873 British Holstein-Friesian heifers, the progeny of 40 proven and 649 unproven sires, using restricted maximum likelihood (REML) and Gibbs sampling methods with a univariate sire model. Results from the two methods are then compared. It is found that the posterior expectations and REML estimates of the parameters are fairly similar. The marginal posterior expectation and REML estimate of heritability for lactation milk yield are 0.49 and 0.50, respectively. Heritability estimates for individual test day records range from 0.27 to 0.40, whilst the posterior expectations are between 0.28 and 0.42. Generally, heritabilities for test day records were lowest at the start and highest in the second half of the lactation. Gibbs sampling requires substantially more computing than REML estimation, but provides a more informative analysis.