Application of Bayesian inference in the comparison of lactation curves of Merino ewes

Bayesian theory is applied to compare the characteristics of the estimated lactation curves of two groups of 5-year-old Merino ewes. The diets of the two groups were supplemented respectively by DL-methionine and maleyl-DLmethionine. The purpose is to illustrate the Bayesian approach when analysing for the effect of supplement on the lactation pattern of the sheep. Using Wood's model, the posterior distributions of the model parameters are determined for the two groups. This is achieved by assuming a hierarchical Bayes model and applying the Gibbs sampler, a sampling based computer intensive algorithm that is very efficient in obtaining marginal distributions of functions of parameters. The Gibbs sampler enables us to obtain marginal posterior distribution of characteristics of the lactation curve such as peak yield, time of peak yield, persistency and total milk yield. The results are notable differences in the marginal posterior distributions of mean peak milk yield and mean total yield. The posterior probability that the mean peak milk yield of the group supplemented by maleyl-DL-methionine is higher than that of the group with DL-methionine supplement is 0·98, while the same probability for mean total yield is 0·83.