596
个编辑
更改
无编辑摘要
</syntaxhighlight>
</syntaxhighlight>
'''Monte Carlo and random numbers'''
The main idea behind this method is that the results are computed based on repeated random sampling and statistical analysis. The Monte Carlo simulation is, in fact, random experimentations, in the case that, the results of these experiments are not well known. Monte Carlo simulations are typically characterized by many unknown parameters, many of which are difficult to obtain experimentally. Monte Carlo simulation methods do not always require truly random numbers to be useful (although, for some applications such as primality testing, unpredictability is vital). Many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense.
The main idea behind this method is that the results are computed based on repeated random sampling and statistical analysis. The Monte Carlo simulation is, in fact, random experimentations, in the case that, the results of these experiments are not well known. Monte Carlo simulations are typically characterized by many unknown parameters, many of which are difficult to obtain experimentally. Monte Carlo simulation methods do not always require truly random numbers to be useful (although, for some applications such as primality testing, unpredictability is vital). Many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense.
这种方法的主要思想是基于重复随机抽样和统计分析来计算结果。蒙特卡洛模拟实际上是一种随机实验，在这种情况下，这些实验的结果并不为人所知。蒙特卡罗模拟的典型特征是有许多未知参数，其中许多参数很难通过实验获得。蒙特卡罗模拟方法并不总是要求真正的随机数是有用的(尽管对于一些应用程序，如质数测试，不可预测性是至关重要的)。许多最有用的技术使用确定性的伪随机序列，使测试和重新运行模拟变得很容易。伪随机序列在某种意义上表现地“足够随机”，这是进行良好模拟所必需的唯一品质。
What this means depends on the application, but typically they should pass a series of statistical tests. Testing that the numbers are uniformly distributed or follow another desired distribution when a large enough number of elements of the sequence are considered is one of the simplest and most common ones. Weak correlations between successive samples are also often desirable/necessary.
What this means depends on the application, but typically they should pass a series of statistical tests. Testing that the numbers are uniformly distributed or follow another desired distribution when a large enough number of elements of the sequence are considered is one of the simplest and most common ones. Weak correlations between successive samples are also often desirable/necessary.
所谓“足够随机”的含义一般取决于应用场景，但通常也应该通过一系列统计测试。当需要考虑的序列中元素足够多时，检验这些数是均匀分布的，还是遵循另一个期望的分布是最简单常见的方法之一。连续样本之间的弱相关性通常也是可取的，或必要的。
Sawilowsky lists the characteristics of a high-quality Monte Carlo simulation:
Sawilowsky lists the characteristics of a high-quality Monte Carlo simulation:
萨维罗斯基 Sawilowsky列出了高质量蒙特卡罗模拟的特点：
'''萨维罗斯基 Sawilowsky'''列出了高质量蒙特卡罗模拟的特点：
*the (pseudo-random) number generator has certain characteristics (e.g. a long "period" before the sequence repeats)
*the (pseudo-random) number generator has certain characteristics (e.g. a long "period" before the sequence repeats)
*(伪随机数)生成器具有某些特征(例如，序列重复之前有一个很长的“周期”)
*the (pseudo-random) number generator produces values that pass tests for randomness
*the (pseudo-random) number generator produces values that pass tests for randomness
*(伪随机数)生成器生成能通过随机性测试的值
*there are enough samples to ensure accurate results
*there are enough samples to ensure accurate results
*有足够的样本来确保准确的结果
*the proper sampling technique is used
*the proper sampling technique is used
*使用适当的取样技术
*the algorithm used is valid for what is being modeled
*the algorithm used is valid for what is being modeled
*使用的算法对建模内容是有效的
*it simulates the phenomenon in question.
*it simulates the phenomenon in question.
*它可以对问题中的现象进行模拟。
[[Pseudo-random number sampling]] algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed according to a given [[probability distribution]].
[[Pseudo-random number sampling]] algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed according to a given [[probability distribution]].