This book is a compilation of unpublished papers written by Jean-Marie Rolin (with several co-authors) on nonparametric bayesian estimation. Jean-Marie was professor of statistics at University of Louvain and died on November 5th, 2018. He made important contributions in mathematical statistics with applications to different fields like econometrics or biometrics.These papers cover a variety of topics, including:

• The Mathematical structure of the Bayesian model and the main concepts (sufficiency, ancillarity, invariance…)

• Representation of the Dirichlet processes and of the associated Polya urn model and applications to nonparametric bayesian analysis.

• Contributions to duration models and to their non parametric bayesian treatment.