Approximately counting and sampling knowledge states from a knowledge space is a problem that is of interest for both applied and theoretical reasons. However, many knowledge spaces used in practice are far too large for standard statistical counting and estimation techniques to be useful. Thus, in this work we use an alternative technique for counting and sampling knowledge states from a knowledge space. This technique is based on a procedure variously known as subset simulation, the Holmes-Diaconis-Ross method, or multilevel splitting. We make extensive use of Markov chain Monte Carlo methods and, in particular, Gibbs sampling, and we analyse and test the accuracy of our results in numerical experiments.

中文翻译：

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近似计数和抽样知识状态。

对知识空间中的知识状态进行近似计数和抽样是一个由于应用和理论原因都令人感兴趣的问题。然而，实践中使用的许多知识空间对于标准统计计数和估计技术来说太大而无法使用。因此，在这项工作中，我们使用一种替代技术来计算和采样知识空间中的知识状态。该技术基于称为子集模拟、Holmes-Diaconis-Ross 方法或多级分裂的各种程序。我们广泛使用马尔可夫链蒙特卡罗方法，特别是吉布斯抽样，并在数值实验中分析和测试我们的结果的准确性。