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近周期马尔可夫链蒙特卡洛算法的渐近方差与收敛速度AI 解读

This article considers nearly-periodic Markov chains that may have excellent functional estimation properties but poor distributional convergence rate. It shows how simple modifications of the chain (involving using a random number of iterations) can greatly improve the distributional convergence of the chain. Various theoretical results about convergence rates of the modified chains are proven. A number of examples, including a transdimensional Markov chain Monte Carlo…

对 Brooks、Giudici 与 Roberts 论文的讨论AI 解读

This paper aims to develop general strategies for improving jumps between models in reversible jump Markov chain Monte Carlo (MCMC) algorithms, which is quite an important and timely goal. Indeed, in practical implementations of the method, we usually find that the choice of proposals is paramount: in many cases, the ‘natural choice’ leads to a zero acceptance probability and the construction of well-tuned moves is often quite costly. Given that the reversible jump MCMC…