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.
Original language | English (US) |
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Pages (from-to) | 1-22 |
Number of pages | 22 |
Journal | Journal of Statistical Computation and Simulation |
DOIs | |
State | Published - Sep 29 2022 |
Externally published | Yes |
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics
- Statistics and Probability
- Statistics, Probability and Uncertainty