Bayesian analysis of lamb survival using Monte Carlo numerical integration with importance sampling.

Approximate and exact Bayesian analyses of survival from birth to weaning measured as an "all or none" trait were conducted on 2,554 Rambouillet lambs using an asymptotic normal approximation and Monte Carlo numerical integration with importance sampling, respectively. A linear logistic model was used to assess the effects of year, age of dam, sex of lamb, and type of birth on the survival probability. A least squares analysis of the data, ignoring their discrete nature, was also performed. The Bayesian analyses were compared by plotting the marginal posterior distributions and by constructing 95% highest-posterior-density regions for some parameters of interest. The analyses were repeated for a reduced data set consisting of 300 observations selected at random from the original file. For all practical purposes, the Bayesian and non-Bayesian analyses yielded identical results despite their different interpretations. Also, the asymptotic normal approximations to the true posterior distributions were excellent. Undoubtedly, this is because the likelihood functions contained a large amount of information about the parameters. Four-year-old ewes produced lambs with greater survival rates than either younger or older ewes. Female and male lambs had similar rates, and single-born lambs had a 10% higher survival rate than multiple-born lambs.