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Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

机译：嘈杂的蒙特卡洛：具有近似过渡核的马尔可夫链的收敛

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摘要

MonteCarlo algorithms often aim to draw from a distribution pi by simulating a Markov chain with transition kernel P such that pi is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation (P) over cap. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel (P) over cap is to the chain given by P. We apply these results to several examples from spatial statistics and network analysis.
机译：MonteCarlo算法通常旨在通过模拟具有过渡核P的马尔可夫链来从分布pi进行绘制，使得pi在P下不变。但是，在许多情况下，从过渡核P进行绘制是不切实际或不可能的。 ，对于海量数据集来说就是这种情况，在这种情况下，计算似然性的成本过高，对于由诸如空间统计和网络分析中的吉布斯随机场等产生的顽固似然模型也是如此。在这些情况下，自然的做法是用上限的近似值（P）代替P。使用来自马尔可夫链稳定性的理论，我们探索了各种情况，在这种情况下，有可能量化过渡核（P）所提供的上限与P所提供的链之间的“接近”程度。我们将这些结果应用于几种情况空间统计和网络分析中的示例。

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