Recent research has led to the development of MCMC algorithms with likelihood-informed proposals when targeting posterior distributions supported on discrete state spaces. Our work is placed within this field and puts forward a new MCMC methodology based upon similarity-driven proposals. Such proposals sway transitions towards states favored by the posterior via use of a data-driven measure of discrepancy between observations and the proposed model. Our approach can naturally cover classes of hierarchical models that involve both discrete variables and additional latent ones, without a requirement of integrating our the latter, in contrast to previous works in this field. The new algorithms are illustrated in simulation settings and in a involved real data scenario with a Dirichlet-Multinomial regression model.

翻译：近期研究推动了针对离散状态空间后验分布的MCMC算法发展，此类算法利用似然驱动建议进行采样。本研究立足该领域，提出了一种基于相似性驱动建议的新型MCMC方法。该方法通过引入观测数据与提议模型之间的数据驱动差异度量，促使马尔可夫链向更受后验支持的转移状态移动。与以往研究相比，我们的方法可自然覆盖包含离散变量与潜变量的分层模型类别，且无需对潜变量进行积分处理。通过仿真实验及Dirichlet-Multinomial回归模型的实际复杂数据场景，验证了新型算法的有效性。