AbstractEstimation of a smooth function is considered when observations on this function added with Gaussian errors are observed. The problem is formulated as a general linear model, and a hierarchical Bayesian approach is then used to study it. Credible bands are also developed for the function. Sensitivity analysis is conducted to determine the influence of the choice of priors on hyperparameters. Finally, the methodology is illustrated using real and simulated examples where it is compared with classical cubic splines. It is also shown that our approach provides a Bayesian solution to some problems in discrete time series.