Three general approaches leading to the marginal posterior probability distribution function for the autocorrelation coefficient of the first order annual autoregressive model are presented, based on varying assumptions about the incidental parameters of the model. The performance of the Bayes estimators for the quadratic, symmetric, linear and asymmetric linear loss functions is evaluated by Monte Carlo methods, and compared to the performance of some classical estimators, under the expected risk criterion and for conditions of limited data. The robustness of the Bayes estimator under changes of the loss function is also determined. The general framework for the derivation of a loss function for a hydrologic design problem is presented. (Author)