可逆跳马尔可夫链蒙特卡罗计算中跳方案的一种有效插值技术
An Efficient Interpolation Technique for Jump Proposals in Reversible-Jump Markov Chain Monte Carlo Calculations
摘要：
在物理学和天文学的许多领域中，在给定观测数据集的情况下选择替代理论模型是一个重要的挑战。可逆跳马尔可夫链蒙特卡罗（RJMCMC）是一种非常强大的贝叶斯模型选择技术，但它有一个根本的困难：它需要在模型参数空间之间进行跳跃，但不能同时有效地探索两个参数空间。因此，在MCMC算法中不太可能接受参数空间之间的朴素跳跃，并且收敛相应地慢。在这里，我们展示了一种插值技术，使用单模型MCMCCs的样本提出从目标参数空间的单模型后验近似的模型间跳跃。插值技术，基于kD树数据结构，是自适应的和有效的适度的维数。我们表明，我们的技术导致改进的收敛在一个RJMCMC天真的跳跃，并比较它在文献中的其他建议，以提高收敛的RJMCMC。我们还演示了使用相同的插值技术作为一种方式来构建有效的“全球”建议分布的单模型MCMCCs没有先验知识的后验分布的结构，并讨论了改进，允许该方法被有效地用于高维空间。
英文摘要：
Selection among alternative theoretical models given an observed data set is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty: it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the MCMC algorithm and convergence is correspondingly slow. Here we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose inter-model jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient "global" proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher-dimensional spaces efficiently.
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