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arXiv · 2107.07313

The Taxicab Sampler: MCMC for Discrete Spaces with Application to Tree Models

Vincent Geels·Matthew Pratola·Radu Herbei
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Abstract

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: 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 related Hamming ball sampler. The proposed sampling algorithm is then shown to demonstrate substantial improvement in computation time without any loss of efficiency relative to a na\"ive 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.

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Vincent Geels, Matthew Pratola, Radu Herbei. 2021-07-15. The Taxicab Sampler: MCMC for Discrete Spaces with Application to Tree Models. https://doi.org/10.1080/00949655.2022.2119972

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