Maximum likelihood estimation of the parameters of the prior distributions of three variables that strongly influence reproductive performance in cows.

Ovulation detection rate, pregnancy rate, and embryo loss rate greatly affect the reproductive performance of cows. A previous model described the separate effects of these variables on the resulting calving patterns and assumed that the variables have the same value for all cows belonging to the same herd. This is not a realistic biological assumption, so the beta distribution is used to introduce "between-cow" variation in the three variables. Two approaches are used to find maximum likelihood estimates of the parameters of these prior beta distributions. The first considers sequences of ovulations, artificial inseminations, and pregnancies, separately. For both ovulation detection rate and pregnancy rate this approach considers the number of "successes" of each event for a particular cow (e.g., in the case of an ovulation, a success is a detection), and conditions on the total number of occurrences of that event in the cow, so that beta-binomial distributions are considered. However, for embryo loss rate the number of pregnancies required until a particular cow calves is considered, so that a beta-geometric distribution results. If the cow is removed before she calves, a censored sequence will result. The second approach considers the sequences of ovulations, artificial inseminations, pregnancies, and embryo losses, together, which will stop only when the cow calves. Otherwise, if she is removed before that time, a censored sequence will result. In this case, a joint distribution, with three independent prior beta distributions, is considered. The results of the analysis of data from 22 herds are discussed.