Comment on article by Jain and Neal
Christian P. Robert · Bayesian Analysis · 2007
From a stylistic point of view, I think this paper reads very much like a sequel to the important paper Jain and Neal (2004) and therefore it is not exactly self-contained since the main bulk of the paper is a commentary of the program provided in Section 4.2. Instead of the current version, I would thus have preferred a truly self-contained version with a more user-friendly introduction, for instance when reading and re-reading Sections 3 and 4.1... 1 The central point of the paper is to extend Jain and Neal (2004) so that the lack of complete conjugacy of the prior does not prevent the algorithm from being run. Indeed, in Jain and Neal (2004), the model parameters are completely hidden in that the likelihood and the prior only depend on the cluster index vector c, which means working in a finite set. The difficulty with priors G0 that do not lead to closed form marginals is that the parameters must take part in the simulation process. The idea at the core of the current paper is to take advantage of the conditional conjugacy, i.e. the fact that the prior on a given parameter is still conjugate and thus manageable, conditional on all the other parameters, so that a Gibbs sampling version can be implemented.