ACCURATE MONTE CARLO ESTIMATION OF VERY SMALL VALUES IN MARKOV CHAINS

在真实的世界里有很多事情 从随机。如果我们可以根据它们的重要性来分配它们， 在严格的随机模型中，这样的p值必须非常小 的确.我们为什么要对这么小的数字感兴趣？ 基本上是因为这个数字是对预期数量的估计 必须添加到随机模型中， 确定所讨论的事件。这样的自我信息提供了一个 估计事件的复杂性，并可用于排名 在人类检查之前，按感兴趣的顺序排列事件。在一些 在某些情况下，我们可以从封闭公式中确定非常小的p值。 在其他情况下，适当的随机模型足以 复杂的是，我们不能这样做。我们已经开发了一种算法 它允许我们计算一些非常小的p值， 复杂的随机模型，可以实现为马尔可夫 流程.已经研究了三个例子，说明了 算法的性能。发表了一篇文章。工作 正在继续将该算法应用于 蛋白质结构模型中的信息。

There are many events in the real world that are far from random. If we could assign significance levels to them based on a rigorous random model, such p-values must be very small indeed. Why should we be interested in such small numbers? Basically because the number is an estimate of the expected amount of information in bits that must be added to the random model to determine the event in question. Such self information provides an estimate of the complexity of the event and may serve to rank events in order of interest prior to human examination. In some cases we can determine very small p-values from closed formulas. In other cases the appropriate random model is sufficiently complicated that we cannot do so. We have developed an algorithm that allows one to calculate very small p-values for some complicated random models that can be realized as Markov processes. Three examples have been studied illustrating the performance of the algorithm. An article has been published. Work is continuing on the application of this algorithm to the estimates of information in protein structural models.