| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | B. (i) and (iii) only Explanation: Antithetic variates is a technique used in Monte Carlo experiments to reduce the variance of the estimates. It involves using the negative of each of the random draws and repeating the experiment using those values as the draws. This helps to cover the whole probability space more efficiently, reducing the number of replications required. Statement (i) is correct, as antithetic variates do reduce the number of replications required to cover the whole probability space. Statement (iii) is also correct, as antithetic variates involve using the negative of each of the random draws and repeating the experiment using those values as the draws. Statement (ii) is incorrect, as antithetic variates do not involve employing a similar variable to that used in the simulation, but whose properties are known analytically. Statement (iv) is also incorrect, as antithetic variates do not involve taking one over each of the random draws and repeating the experiment using those values as the draws. Therefore, the correct answer is B. (i) and (iii) only. |
B |
| deepseekr1 | The correct answer is **B. (i) and (iii) only**. **Explanation:** - **Statement (i)** is correct because antithetic variates reduce variance by introducing negative correlation between pairs of simulations. This allows achieving the same precision with fewer replications, effectively reducing the number required. - **Statement (iii)** is correct in contexts where the distribution is symmetric (e.g., normal variables). Using the negative of random draws (e.g., \(Z\) and \(-Z\)) creates the necessary negative correlation, which aligns with the antithetic variate method for such distributions. - **Statement (ii)** is incorrect because antithetic variates do not rely on variables with analytically known properties (this describes control variates, a different technique). - **Statement (iv)** is incorrect because taking reciprocals (1/U) of random draws does not align with antithetic variates; instead, transformations like \(1-U\) (for uniform variables) or \(-Z\) (for normal variables) are used. Thus, only statements (i) and (iii) are correct. **Answer:** B |
B |
| gpto1 | B | B |
| GPT-4o | B. (i) and (iii) only | B |
| llama3.1-70B-Instruct | B |
B |
| llama3.1-405B-Instruct | B |
B |
| DeepSeek-Coder-V2 | B | B |
| Qwen2-72B-Instruct | B. (i) and (iii) only | B |
| baichuan4 | B. (i) and (iii) only | B |
| doubao | B Antithetic variates involve using the negative of each of the random draws and repeating the experiment using those values as the draws, which helps reduce variance and can be considered as a way to make better use of the replications rather than reducing the number of replications to cover the whole probability space. Statement (ii) is not correct as it does not accurately describe the concept of antithetic variates. Statement (iv) is also incorrect. So only (i) and (iii) are correct. |
B |
| minimax | B. (i) and (iii) only Antithetic variates are a variance reduction technique used in Monte Carlo simulations. They work by pairing each random draw from a distribution with its antithetic counterpart, which is typically the negative of that draw. This pairing is done to reduce the variance of the simulation's output. The idea is that if one draw is above the mean, its antithetic counterpart is likely to be below the mean, and their average will be closer to the mean of the distribution, thus reducing the variance. This technique can indeed reduce the number of replications required to achieve a given level of precision in the estimates. Statement (ii) is incorrect because antithetic variates do not involve a similar variable with known analytical properties; they involve the same variable with its negative counterpart. Statement (iv) is incorrect because taking the reciprocal (one over) of each draw is not a characteristic of antithetic variates. |
B |
| kimi | B. (i) and (iii) only Antithetic variates are a variance reduction technique used in Monte Carlo simulations. They work by pairing each random variate with its antithetic counterpart to reduce the variance of the simulation's output. Here's a brief explanation of each statement: i) Antithetic variates can indeed reduce the variance of the simulation's output, which can lead to a reduction in the number of replications needed to achieve a certain level of accuracy or confidence in the results. ii) This statement is incorrect. Antithetic variates do not necessarily involve a variable with known analytical properties. They are simply the opposites of the original random variates. iii) This statement is correct. Antithetic variates often involve using the negative of each random draw. For example, if a random draw is positive, the antithetic variate would be the same amount but negative. iv) This statement is incorrect. Taking the reciprocal of each random draw is not a standard practice for creating antithetic variates. It would not generally be expected to reduce variance in the same way as using the negative of the draws. |
B |
| wenxinyiyan | B. (i) and (iii) only Explanation: Antithetic variates are a variance reduction technique used in Monte Carlo simulation. The basic idea is to create a negative correlation between pairs of random variables, which can help to reduce the variance of the simulation estimator. i) This statement is correct. By introducing negative correlation, antithetic variates can effectively cover the probability space more efficiently, thereby reducing the number of replications required to achieve a given level of precision. ii) This statement is incorrect. Antithetic variates do not involve using a similar variable with analytically known properties. Instead, they involve generating pairs of random variables that are negatively correlated. iii) This statement is correct. A common way to implement antithetic variates is to take the negative of each random draw (or, in the case of a bounded variable, such as a uniform variate, to use the complement within the bounds) and repeat the experiment using those values. iv) This statement is incorrect. Taking one over each of the random draws is not part of the antithetic variates technique. The key idea is to introduce negative correlation, which is typically achieved by using the negative (or complement) of the original draws, not by taking their reciprocals. |
B |
| zhipu | B. (i) and (iii) only Explanation: - Statement (i) is correct because antithetic variates help reduce the variance of the estimator, which can effectively reduce the number of replications needed to achieve a certain level of precision. - Statement (iii) is correct because antithetic variates typically involve using the negative of each of the random draws to create pairs of dependent observations that reduce the variability of the simulation results. - Statement (ii) is incorrect because antithetic variates do not necessarily involve a variable whose properties are known analytically. - Statement (iv) is incorrect because taking one over each of the random draws is not the standard approach used in antithetic variates. Therefore, the correct choice is B. |
B |
| gpto1 | B | B |