  Abstract. Whenever a new approach to perform Bayesian computation is
introduced, a common practice is to showcase this approach on a binary
regression model and datasets of moderate size. This paper discusses to which
extent this practice is sound. It also reviews the current state of the art of
Bayesian computation, using binary regression as a running example. Both
sampling-based algorithms (importance sampling, MCMC and SMC) and fast
approximations (Laplace and EP) are covered. Extensive numerical results are
provided, some of which might go against conventional wisdom regarding the
effectiveness of certain algorithms. Implications for other problems (variable
selection) and other models are also discussed.
