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.
翻译:基于探索巴伊西亚模式中离散但非常复杂的国家空间的问题,我们提议了一部新颖的Markov链条蒙特卡洛搜索算法:计税器取样员。我们描述了该取样员的构造,并讨论了其解释和使用与标准大都会-哈斯廷以及相关的哈明球取样员的不同之处。然后,拟议的采样算法显示,在计算时间方面有很大的改进,而相对于一个激励巴伊西亚回归树计数模型而言,效率没有任何损失。 在这个模型中,我们利用离散状态空间假设来构建一个新的可能性功能,允许灵活描述不同的中位差异关系,同时保持参数与现有计数数据的概率函数相比的可解释性。