论文标题
MCMC和其他蒙特卡洛方法的单元测试
Unit Testing for MCMC and other Monte Carlo Methods
论文作者
论文摘要
我们提出了测试马尔可夫链蒙特卡洛方法的实施的方法以及一般的蒙特卡洛方法。基于统计假设测试，这些方法可以在单元测试框架中使用，例如检查Gibbs采样器中的单个步骤还是可逆的跳跃MCMC具有所需的不变分布。讨论了评估给定的马尔可夫链是否具有指定不变分布的两个精确测试。这些和其他蒙特卡洛方法的测试可以嵌入到一个顺序方法中，如果模拟显示所需的行为和高功率，则可以允许较低的预期工作。此外，错误的拒绝概率可以任意保持较低。对于一般的蒙特卡洛方法，这允许测试，例如，如果采样器具有指定的分布或采样器产生所需平均值的样品。这些方法已在R-Package McUnit中实现。
We propose approaches for testing implementations of Markov Chain Monte Carlo methods as well as of general Monte Carlo methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for example, check if individual steps in a Gibbs sampler or a reversible jump MCMC have the desired invariant distribution. Two exact tests for assessing whether a given Markov chain has a specified invariant distribution are discussed. These and other tests of Monte Carlo methods can be embedded into a sequential method that allows low expected effort if the simulation shows the desired behavior and high power if it does not. Moreover, the false rejection probability can be kept arbitrarily low. For general Monte Carlo methods, this allows testing, for example, if a sampler has a specified distribution or if a sampler produces samples with the desired mean. The methods have been implemented in the R-package MCUnit.
