BAYESIAN-ANALYSIS OF LAMB SURVIVAL USING MONTE-CARLO NUMERICAL-INTEGRATION WITH IMPORTANCE SAMPLING

Approximate and exact Bayesian analyses of survival from birth to wean ing measured as an ''all or none'' trait were conducted on 2,554 Rambo uillet 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, se x of lamb, and type of birth on the survival probability. A least squa res analysis of the data, ignoring their discrete nature, was also per formed. The Bayesian analyses were compared by plotting the marginal p osterior distributions and by constructing 95% highest-posterior-densi ty regions for some parameters of interest. The analyses were repeated for a reduced data set consisting of 300 observations selected at ran dom from the original file. For all practical purposes, the Bayesian a nd non-Bayesian analyses yielded identical results despite their diffe rent interpretations. Also, the asymptotic normal approximations to th e true posterior distributions were excellent. Undoubtedly, this is be cause 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 lamb s had similar rates, and single-born lambs had a 10% higher survival r ate than multiple-born lambs.