Monte Carlo methods
Monte Carlo methods
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DOI：
10.1007/s13137-017-0101-z
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发表时间：
2017-12
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影响因子：
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通讯作者：
K. Koch
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文献类型：
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作者：
K. Koch
蒙特卡罗方法处理从概率密度函数生成随机变量，以估计未知参数或未知参数的一般函数，并计算其期望值，方差和协方差。由于中心极限定理，人们通常使用多元正态分布。但是，如果将具有正态分布的随机变量和具有不同分布的随机变量组合，则正态分布不再有效。本文讨论了Monte Carlo方法的误差传播问题，给出了由多元正态分布和多元均匀分布生成随机变量的方法。蒙特卡洛积分导致抽样重要性恢复（SIR）算法。马尔可夫链蒙特卡罗方法通过大都会算法和吉布斯采样器提供了生成随机变量的其他方法。一个特别的主题是用于计算和传播大型协方差矩阵的吉布斯采样器。当地球位势是由卫星观测确定的时候，这个任务就产生了。最小可检测离群值的示例显示了如何使用蒙特卡罗方法来确定假设检验的功效。
Monte Carlo methods deal with generating random variates from probability density functions in order to estimate unknown parameters or general functions of unknown parameters and to compute their expected values, variances and covariances. One generally works with the multivariate normal distribution due to the central limit theorem. However, if random variables with the normal distribution and random variables with a different distribution are combined, the normal distribution is not valid anymore. The Monte Carlo method is then needed to get the expected values, variances and covariances for the random variables with distributions different from the normal distribution.The error propagation by the Monte Carlo method is discussed and methods for generating random variates from the multivariate normal distribution and from the multivariate uniform distribution. The Monte Carlo integration is presented leading to the sampling-importance-resampling (SIR) algorithm. Markov Chain Monte Carlo methods provide by the Metropolis algorithm and the Gibbs sampler additional ways of generating random variates. A special topic is the Gibbs sampler for computing and propagating large covariance matrices. This task arises when the geopotential is determined from satellite observations. The example of the minimal detectable outlier shows, how the Monte Carlo method is used to determine the power of a hypothesis test.