The taxicab sampler: MCMC for discrete spaces with application to tree models

Motivated by the problem of exploring discrete but very complex state spaces in Bayesian models, we propose a novel Markov Chain Monte Carlo search algorithm: taxicab sampler. We describe construction this sampler and discuss how its interpretation usage differs from that standard Metropolis-Hastings as well related Hamming ball The proposed sampling algorithm is then shown to demonstrate substantial improvement computation time without any loss efficiency relative na\"ive motivating regression tree count model, which leverage space assumption construct likelihood function allows for flexibly describing different mean-variance relationships while preserving parameter interpretability compared existing functions data.