Discussion on Walker, Damien, Laud and Smith

Abstract

models. In practice, it is likely that these algorithms will not be commonly used and I am going to concentrate my remarks on the other two constructions presented for which prior to posterior computations are fairly straightforward. Note that both P'olya trees (PT) and Bernoulli trips (BT) involve in fine some arbitrary discretization, PT will be partially specified up to a level M , while BT rely on discrete time. P'olya tree priors require a binary tree partitioning of the space. In contrast to the DP, it has long been recognized (Ferguson 1974) that the points of subdivisions play a part in the posterior properties of the process, which is an undesirable feature. On the other hand, in comparison to the DP, P'olya trees are more flexible since they allow choice of ff ffl0 ; ff ffl1 at each level, whereas for the DP ff ffl = ff ffl0 + ff<F14