Estimates and posterior distributions of genetic and phenotypic variance matrices for test day milk records are obtained for 23 873 British Holstein-Friesian heifers, the progeny of 40 proven and 649 unproven sires, using restricted maximum likelihood (REML) and Gibbs sampling methods with two different prior specifications in a multivariate sire model. Results from the two methods are then compared. The REML estimates and posterior expectations of heritability and individual test day records range from 0.28 to 0.42. Generally, heritabilities for test day records are lowest at the start and highest in the second half of the lactation. Estimates of genetic correlations between test day milk yields range from 0.59 to 0.99, whilst those of phenotypic correlations are between 0.30 and 0.76, the correlations being highest for adjacent tests. Bayesian inferences are more informative, but require much more computer time.