B1669
Title: The taxicab sampler: MCMC for discrete spaces with application to tree models
Authors: Vincent Geels - The Ohio State University (United States) [presenting]
Matthew Pratola - The Ohio State University (United States)
Radu Herbei - The Ohio State University (United States)
Abstract: Motivated by the problem of exploring discrete but very complex state spaces in Bayesian models, a novel Markov Chain Monte Carlo search algorithm is proposed: the taxicab sampler. We describe the construction of this sampler and discuss how its interpretation and usage differs from that of standard Metropolis-Hastings as well as the closely-related Hamming ball sampler. The proposed taxicab sampling algorithm is then shown to demonstrate substantial improvement in computation time relative to a naive Metropolis-Hastings search in a motivating Bayesian regression tree count model, in which we leverage the discrete state space assumption to construct a novel likelihood function that allows for flexibly describing different mean-variance relationships while preserving parameter interpretability compared to existing likelihood functions for count data.
