ERROR-ESTIMATES ON AVERAGES OF CORRELATED DATA
ERROR-ESTIMATES ON AVERAGES OF CORRELATED DATA
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DOI：
10.1063/1.457480
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发表时间：
1989-07-01
影响因子：
4.4
通讯作者：
PETERSEN, HG
中科院分区：
文献类型：
--
作者：
FLYVBJERG, H;PETERSEN, HG
通过蒙特卡罗方法或分子动力学的物理系统的计算机模拟通常产生相关数据的有限时间序列形式的原始数据。在广泛的情况下，在稳态调查，在数据分析的第一步包括计算时间平均值。由于这样的平均值是超有限时间，它们是波动量：同一系统的另一个模拟通常会为相同的量给出不同的值。因此，数据分析的下一步是估计有限时间平均值的方差。围绕这一问题形成了一种混合做法。相关数据的时间平均误差的流行估计是基于这些数据的相关函数。实际上有一个这样的估计，所有的近似两个原始估计之一的整个家庭。他们在SEC审查。第三，本文与一些注意支付的近似，SUbjective的选择，和计算的努力。这应该使读者理解另一种选择，即“分块”或“聚束”方法，见。四.在我们看来，这种方法结合了最大的严谨性与最小的计算和反思。它不涉及主观选择的近似，当从正在分析的时间序列中可以得到正确答案时，自动给出正确答案，并在情况并非如此时警告用户。我们也给一些希望连续的例子，分析的（见。V和VI）以及数值（见。第七和第八条）。节中IX我们描述了不能使用阻塞方法的情况。读者只需要了解阻塞方法的诀窍，只需要阅读Secs。二，四，九，和一些方程在第二节。三、”堵”法不是我们发明的。它是模拟社区的口头传统的一部分。它可能是K发明的。威尔逊这似乎是合理的，因为它本质上是一个真实的空间重整化群技术应用于一维，离散空间的模拟时间。Whitmer2和Gottlieb等人简要描述了该方法。最近，我们意识到该方法在模拟社区的部分地区是未知的，因此我们在这里详细描述了该方法。
Computer simulations of physical systems by Monte Carlo methods or molecular dynamics typically produce raw data in the form of finite time series of correlated data. In the wide class of cases, where stationary states are investigated, the first step in the data analysis consists in computing time averages. Since such averages are overfinite times, they are fluctuating quantities: another simulation of the same system will typically give a different value for the same quantity. So the next step in the data analysis consists in estimating the variance of finite time averages. A mixed practice has developed around this problem. A popular estimator for the error on a time average of correlated data is based on the correlation function for these data. There is actually a whole family of such estimators, all being approximations to one of two original estimators. They are reviewed in Sec. III of this paper with some attention paid to the approximations, SUbjective choices, and computational effort involved. That should make the reader appreciate the alternative, the" blocking," or" bunching," method, described in See. IV. In our opinion this method combines maximum rigor with minimum computation and reflection. It involves no approximations for SUbjective choices, automatically gives the correct answer, when it is available from the time series being analyzed, and warns the user, when this is not the case. We also give some-hopefully illustrative-examples, analytical ones (Sees. V and VI) as well as numerical ones (Sees. VII and VIII). In Sec. IX we describe situations in which the blocking method cannot be used. The reader, who wants just a recipe for the blocking method, needs only read Secs. II, IV, and IX, and a few equations in Sec. III.The" blocking" method was not invented by us. It is part of the verbal tradition in a part of the simulation community. It may have been invented by K. Wilson. I This seems plausible, since it is essentially a real space renormalization group technique applied in the one-dimensional, discrete space of simulation time. The method is briefly described by Whitmer2 and Gottlieb et aP Recently, we were made aware that the method is unknown in parts of the simulation community, and it is upon request that we describe it in some detail here.