论文标题
马尔可夫链中的多元强不变性原理蒙特卡洛
Multivariate strong invariance principles in Markov chain Monte Carlo
论文作者
论文摘要
马尔可夫链蒙特卡洛中强的不变性原理对于理论上扎根的输出分析至关重要。使用该过程的宽强度再生性质，我们获得了强大的不变性融合率的明确界限，用于多变量ergodic马尔可夫链的部分总和。因此，我们介绍了关于多项式和几何刻板的马尔可夫链的强大不变性原理的结果，而无需1步较小的条件。我们的紧张和明确的速率对产出分析有直接影响，因为它允许在某些方差估计器的强一致性中验证重要条件。
Strong invariance principles in Markov chain Monte Carlo are crucial to theoretically grounded output analysis. Using the wide-sense regenerative nature of the process, we obtain explicit bounds in the strong invariance converging rates for partial sums of multivariate ergodic Markov chains. Consequently, we present results on the existence of strong invariance principles for both polynomially and geometrically ergodic Markov chains without requiring a 1-step minorization condition. Our tight and explicit rates have a direct impact on output analysis, as it allows the verification of important conditions in the strong consistency of certain variance estimators.
