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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.

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。

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.

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)

*the (pseudo-random) number generator produces values that pass tests for randomness

*the (pseudo-random) number generator produces values that pass tests for randomness

*there are enough samples to ensure accurate results

*there are enough samples to ensure accurate results

*the proper sampling technique is used

*the proper sampling technique is used

*the algorithm used is valid for what is being modeled

*the algorithm used is valid for what is being modeled

*it simulates the phenomenon in question.

*it simulates the phenomenon in question.

[[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]].