The taxicab sampler: MCMC for discrete spaces with application to tree models. Issue 5 (24th March 2023)

• Record Type: Journal Article
• Authors: Geels, Vincent; Pratola, Matthew T.; Herbei, Radu
• Is Part Of: Journal of statistical computation and simulation. Volume 93:Issue 5(2023)
• Page Start: 753
• Page End: 774
• Publication Date: 2023-03-24
• Subjects: Discrete state spaces -- Markov Chain Monte Carlo -- regression trees -- count data -- data augmentation; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2022.2119972
• Languages: English
• ISSNs: 0094-9655

Abstract

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 naïve 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.