Inverse Problems and High Dimensional Estimation : Stats in the Château Summer School August 31 September 4 2009 Part I Lecture Notes on Inverse Problems: Inverse Problems in Statistics (Laurent Cavalier) Part II Invited Contribution on Inverse Problems: Non Parametric Models with Instrumental Variables (Jean Pierre Florens) Part III Lecture Notes on High Dimensional Estimation: High Dimensional Sparse Econometric Models: An Introduction (Alexandre Belloni and Victor Chernozhukov) Part IV Invited Contributions on High Dimensional Estimation: Model selection in Gaussian regression for high dimensional data (Felix Abramovich and Vadim Grinshtein) Bayesian Perspectives on Sparse Empirical Bayes Analysis (SEBA) (Natalia Bochkina and Ya’acov Ritov) Part V Invited and Contributed Talks Given During the Summer School: List of the Courses List of the Invited Talks List of the Contributed Talks and Posters. The “Stats in the Château” summer school was held at the CRC château on the campus of HEC Paris Jouy en Josas France from August 31 to September 4 2009. This event was organized jointly by faculty members of three French academic institutions ─ ENSAE ParisTech the Ecole Polytechnique ParisTech and HEC Paris ─ which cooperate through a scientific foundation devoted to the decision sciences. The scientific content of the summer school was conveyed in two courses one by Laurent Cavalier (Université Aix Marseille I) on Ill posed Inverse Problems and one by Victor Chernozhukov (Massachusetts Institute of Technology) on High dimensional Estimation with Applications to Economics . Ten invited researchers also presented either reviews of the state of the art in the field or of applications or original research contributions. This volume contains the lecture notes of the two courses. Original research articles and a survey complement these lecture notes. Applications to economics are discussed in various contributions.