Abstract
While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures. Recent innovations like Monte Carlo Markov chain, sequential Monte Carlo methods and more recently Approximate Bayesian Computation techniques have considerably increased the potential for Bayesian applications and they have also opened new avenues for Bayesian inference, first and foremost Bayesian model choice.