Sequential Bayes estimation algorithm with cubic splines on uniform meshes

After outlining the principles of some recent developments in parameter estimation, a sequential numerical algorithm for generalized curvefitting applications is presented combining results from statistical estimation concepts and spline analysis. Using Bayes recursive estimation theory cubic cardinal splines are applied as a flexible linear model, which is designed as a very suitable tool for scientific dataprocessing problems. Due to its recursive nature, the algorithm can be used most efficiently in online experimentation: on the one hand the resulting experimental information can be easily updated after each new observation, on the other hand the recursive procedure allows to control the experiment by means of sequential experimental design techniques. In addition, the algorithm is numerically stable since matrix inversions are avoided. Using computer simulated and experimental data, the efficiency and the flexibility of this sequential estimation procedure is extensively demonstrated