Contributed Discussion on Article by Pratola

Pratola (2016) introduces a novel proposal mechanism for the Metropolis-Hastings step of a Markov chain Monte Carlo (MCMC) sampler that allows efficient traversal of the space of latent stochastic partitions defined by binary regression trees. Here we discuss two considerations: the first is the use of the new proposal mechanism within a population Markov chain Monte Carlo sampler (Geyer, 1991) to further increase sampling efficiency in the presence of greatly separated posterior modes, the second is a prior model that favors parsimony for the problem of variable selection.