This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. The Bayesian Core can be used as a textbook at both undergraduate and graduate levels. It serves as a unique textbook for a service course for scientists aiming at analyzing data the Bayesian way as well as an introductory course on Bayesian statistics.

User's Manual.- Normal Models.- Regression and Variable Selection.- Generalized Linear Models.- Capture-Recapture Experiments.- Mixture Models.- Dynamic Models.- Image Analysis.