Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing flows and density estimation, we demonstrate an approach to enhance the efficiency of RJMCMC sampling by performing transdimensional jumps involving reference distributions. In contrast to other RJMCMC proposals, the proposed method is the first to apply a non-linear transport-based approach to construct efficient proposals between models with complicated dependency structures. It is shown that, in the setting where exact transports are used, our RJMCMC proposals have the desirable property that the acceptance probability depends only on the model probabilities. Numerical experiments demonstrate the efficacy of the approach.

翻译：可逆跳跃马尔可夫链蒙特卡洛（RJMCMC）提议在大多数应用中难以设计出既能实现合理接受率又能保证良好混合性的方案。受近期基于深度神经网络的归一化流与密度估计技术进展的启发，我们提出了一种通过引入参考分布进行跨维度跳跃来提升RJMCMC采样效率的方法。与其他RJMCMC提议不同，本方法首次采用基于非线性传输的途径，在具有复杂依赖结构的模型之间构建高效提议。研究证明，在采用精确传输的场景下，所提出的RJMCMC提议具有理想性质——接受概率仅取决于模型概率。数值实验验证了该方法的有效性。