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Sean711822 · 2024年06月23日

能否解释一下antithetic variates的过程

  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。

老师好，看其他解答还是不太明白这个rerun的过程是什么样的？在antithetic variates的方法中，是否代表一次随机过程要得出两组随机数？（所谓的对偶过程）？这样的话不就相当于时间和模拟次数都翻倍了吗？还是说生产一正一反的两组数据算作一次模拟？这个具体的过程能否解释一下，谢谢！

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1 个答案

李坏_品职助教 · 2024年06月24日

嗨，努力学习的PZer你好：


参考原版书：

Antithetic Variates意思是：其他过程与普通的simulation完全一致，只是每次产生相关系数为负的一对（一对=2个）随机数，如果需要产生b个随机数，只需要做b/2次随机，因为一次随机产生了2个随机数。


而且这俩随机数还是负相关的，会降低sampling error。


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努力的时光都是限量版，加油！

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