Bayesian methods for estimating dose response curves in quantal bioassay are studied. A linearized multi-stage model is assumed for the shape of the curves. A Gibbs sampling approach with data augmentation is employed to compute the Bayes estimates. In addition, estimation of the "relative additional risk" and the "risk specific dose" is studied. Model selection based on conditional predictive ordinates from cross-validated data is developed. Contains 22 references and 8 tables.) (Author)