Summary I Bayesian survival analysis of right-censored survival data is studied using priors on Bern- strin polynomials and Markov chain Monte Carlo methods. These priors easily take into consideration geometric information like convexity or initial guess on the cumulative hazard functions. The support of these priors contains only smooth functions. Certain frequestist asymptotic properties of the posterior distribution are established. Simulation studies indi-cate that these Bayes methods are quite satisfactory. Summary II Bayesian isotonic regressions are studied using priors on Bernstein polynomials and Markov chain Monte Carlo methods. These priors are ?exible and have support the space of bounded, increasing, and continuous functions satisfying certain geometric properties, such as being convex or sigmoidal. As an application, a Baysian isotonic and sigmoidal regression model is successfully employed to conduct data normalization in cDNA microarray exper-iments with DNA control sequences, where calibration curves relating ?uorescence signal intensities to gene expressional levels are studied as regression functions.