Locally linear regression and the calibration problem for Micro-Array analysis

We review the concept of locally linear regression and its relationship to Diday’s Nuées Dynamiques and to tree-structured linear regression. We describe the calibration problem in microarray analysis and propose a Bayesian approach based on tree-structured linear regression. Using the proposed approach, we analyze a subset of a large data set from an Affymetrix microarray calibration experiment. In this example, a tree-structured regression model outperforms a multiple regression model. We calculated 95% Credible Intervals for a sample of the data, obtaining reasonably good results. Future research will consider and compare several other approaches to locally linear regression.