| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | B. (i) and (iii) only Bootstrapping is a method that involves resampling with replacement from the original data to create new samples, which can be used to estimate the distribution of a statistic or a model. It is particularly useful when the distributional properties of the actual data are unknown (iii) or when it is desired that the distributional properties of the data in the experiment are the same as those of some actual data (i). In contrast, pure simulation typically involves generating data from a known distribution, which is not the case when the distributional properties of the actual data are unknown. Therefore, bootstrapping is preferred in situations (i) and (iii). Situation (ii) is not a good fit for bootstrapping, as it requires the distributional properties of the data to be known exactly, which is not the case when using bootstrapping. Situation (iv) is also not a good fit, as bootstrapping can be problematic with very small samples, and other methods such as Monte Carlo simulation may be more suitable. |
B |
| deepseekr1 | B. (i) and (iii) only **Explanation:** - **i)** Bootstrapping resamples from actual data, preserving its distributional properties. Pure simulation requires assuming a distribution, which may not match the actual data. Thus, bootstrapping is preferred here. - **ii)** If exact distributional properties are needed, pure simulation (generating data from a known distribution) is better. Bootstrapping relies on the empirical sample, which approximates but does not guarantee exact properties. - **iii)** When the actual data's distribution is unknown, simulation is infeasible. Bootstrapping is preferred as it uses the empirical distribution. - **iv)** A very small sample reduces bootstrap reliability, and simulation (if the distribution is known) would be better. Bootstrapping is not inherently preferred here unless combined with iii (unknown distribution). Thus, only **i** and **iii** justify preferring bootstrapping. **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. (i) and (iii) only Bootstrapping is a method that involves resampling with replacement from the original data to create new samples, which can be used to estimate the distribution of a statistic or a model's performance. It is particularly useful when the distributional properties of the actual data are unknown (iii) or when it is desired that the distributional properties of the data in the experiment are the same as those of some actual data (i). In contrast, pure simulation typically involves generating data from a known distribution, which may not reflect the actual data's distributional properties. Therefore, bootstrapping is preferred when the distributional properties of the actual data are unknown or need to be preserved. The other options are not correct because: * (ii) If the distributional properties of the data in the experiment are known exactly, pure simulation would be sufficient, and bootstrapping would not be necessary. * (iv) If the sample of actual data available is very small, bootstrapping may not be reliable, and other methods, such as parametric simulation, may be more appropriate. |
B |
| DeepSeek-Coder-V2 | B. (i) and (iii) only | B |
| Qwen2-72B-Instruct | B. (i) and (iii) only | B |
| baichuan4 | B. (i) and (iii) only | B |
| doubao | B Bootstrapping is often preferred when the distributional properties of the actual data are unknown or when the sample of actual data available is small. It helps in estimating properties based on resampling the existing data. Option (ii) where the distributional properties are known exactly would not require bootstrapping as much. So (i) and (iii) only. |
B |
| minimax | D. (i), (ii), (iii), and (iv) | B |
| kimi | B. (i) and (iii) only | B |
| wenxinyiyan | B. (i) and (iii) only Bootstrapping is a statistical technique that involves sampling with replacement from a given dataset to estimate the sampling distribution of a statistic. It is particularly useful when the theoretical distribution of the statistic is unknown or when the sample size is too small to accurately estimate the distribution through other means. Now, let's consider each situation: i) If it is desired that the distributional properties of the data in the experiment are the same as those of some actual data: Bootstrapping is suitable in this case because it preserves the distributional properties of the original data. By sampling with replacement from the actual data, bootstrapping generates new datasets that have similar distributional properties to the original data. ii) If it is desired that the distributional properties of the data in the experiment are known exactly: In this case, pure simulation would be preferred because you can directly generate data from a known distribution. Bootstrapping relies on the distributional properties of the original data, so if you already know the desired distribution, there is no need to use bootstrapping. iii) If the distributional properties of the actual data are unknown: Bootstrapping is useful in this situation because it does not require knowledge of the underlying distribution. By sampling with replacement from the actual data, bootstrapping can provide an estimate of the sampling distribution of a statistic, even when the theoretical distribution is unknown. iv) If the sample of actual data available is very small: While bootstrapping can be used with small sample sizes, its accuracy may be limited. Bootstrapping relies on the available data to estimate the sampling distribution, so if the sample size is very small, the estimates may not be reliable. In this case, pure simulation or other statistical techniques may be more appropriate, depending on the specific context and goals of the analysis. Therefore, based on the above explanations, bootstrapping would be preferred to pure simulation in situations (i) and (iii) only. |
B |
| zhipu | B. (i) and (iii) only Bootstrapping is preferred when: (i) It is desired that the distributional properties of the data in the experiment are the same as those of some actual data, because bootstrapping relies on resampling from the actual data to capture its distributional properties. (iii) The distributional properties of the actual data are unknown, because bootstrapping does not require knowledge of the underlying distribution and can provide estimates based on the empirical distribution of the data. Bootstrapping is not typically preferred in situations (ii) and (iv): (ii) If the distributional properties of the data are known exactly, pure simulation can be more efficient and accurate since it can directly generate data from the known distribution. (iv) If the sample of actual data available is very small, bootstrapping may not be effective because it relies on resampling from the existing data, and a small sample may not adequately represent the population distribution. |
B |
| gpto1 | B | B |