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:实现合理接受率和混合的可翻转的马尔科夫链蒙特卡洛(RJMC )提案在大多数应用中都很难设计。受基于神经网络的深度正常流动和密度估计方面最近进展的启发,我们展示了一种通过使用参考分布进行跨维跳来提高RJMC取样效率的方法。与其他RJMC 提案相比,拟议方法首先采用非线性运输方法,在具有复杂依赖结构的模型之间构建高效的建议书。它表明,在使用精确运输的环境下,我们的RJMC 提案具有可取的属性,即接受概率仅取决于模型概率。数字实验显示了该方法的有效性。</s>