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梦梦 · 2024年05月23日

为什么复制后替换样本数据就能保证重新抽取概率相等？

  1. FRM I
  2. Quantitative

NO.PZ2019040801000068

问题如下：

Analysts' concern for Monte Carlo simulations is the size of the sampling error. Antithetic variate technique is an effective way to reduce the sampling error. In the following statements, which describes the antithetic variate technique most accurately?

选项：

A.

The simulation is rerun using a complement set of the original set of random variables.

B.

The process of data generating is approximated by redefining the unknown variable with a variable that has known properties.

C.

In order to reduce sampling error, analysts enlarges the number of replications.

D.

In order to make sure that the probability of sample data being redrawn is equal, analysts should replace the sample data after every replication.

解释：

A is correct.

考点：Antithetic Variates

解析：本题考查的是关于Antithetic Variates的结论。这句结论“The antithetic variate technique reduces Monte Carlo sampling error by rerunning the simulation using a complement set of the original set of random variables.”在基础班讲义上有。

D说的是为了确保样本数据被重新抽取的概率是相等的，分析员应该在每次复制后替换样本数据。老师，这里不太明白，每次复制是什么意思？能大概描述一下实验过程吗？

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2 个答案

pzqa39 · 2024年05月26日

嗨，从没放弃的小努力你好：


我再来解释一下D选项


D：为了确保样本数据被重新抽取的概率相等，分析人员应当在每次重复实验后更换样本数据。


反向变异技术（Antithetic Variate Technique），作为一种降低抽样误差的方法，并不是通过替换样本数据实现的（D错误原因），而是通过构造一个与原始样本对称（ every replication）的额外样本集来工作的。具体来说，对于每次随机抽样，除了生成一个常规样本外，还会生成一个与之“配对”的样本，这个配对样本通常是通过对原始样本进行某种变换得到的（比如取其相反数，在一定条件下），从而使得两者的误差倾向于互相抵消，达到减小总体估计误差的目的。

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梦梦 · 2024年05月27日

嗯嗯，所以d是错误的

pzqa39 · 2024年05月24日

嗨，爱思考的PZer你好：


在蒙特卡洛模拟中，复制是指对整个模拟过程执行多次（即多个迭代或试验），以获得更稳定的估计。

具体到Antithetic Variate Technique的步骤，可以概括为：

生成原始样本：首先，按照常规方法生成一组随机样本。

构造对偶样本：对于每个原始样本，构造一个“对偶”样本，这通常是通过某种方式反转或变换原始样本得到的，以确保两者具有负相关或至少较低的相关性。

组合样本并计算平均：将每个原始样本与其对应的对偶样本结合，对这组配对样本的函数值求平均，以降低方差。

汇总估计：重复上述过程多次，然后对所有迭代的结果求平均，以得到最终的估计值。

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加油吧，让我们一起遇见更好的自己！

梦梦 · 2024年05月24日

但是复制后替换样本数据是在其中怎么体现的？

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