Warm up

Table of Links

Abstract and 1 Introduction

2 Methodology

2.1 The task

2.2 The communication protocol

2.3 The copula family

3 Pair programming with ChatGPT

3.1 Warm up

3.2 The density

3.3 The estimation

3.4 The sampling

3.5 The visualization

3.6 The parallelization

4 Summary and discussion

5 Conclusion and Acknowledgments

Appendix A: The solution in Python

Appendix B: The solution in R

References

3.1 Warm up

We see that ChatGPT can save our time by quickly and concisely summarizing basic facts about the topic of our interest. We can also limit the size of the answer, which is satisfied in this 91 words long answer. The information about the positive dependence probably follows from what we have already stated before: the negatively dependent models are rarely used in practice, which is probably reflected in ChatGPT’s training data. However, several details of the answer can be discussed. In lines 3 and 4, “random variables” instead of just “variables” would be more precise. From the last sentence, it follows that an Archimedean copula can be expressed as the generator function for some symmetric distributions. This is at least confusing as Archimedean copulas are rather a particular class of copulas admitting a certain functional form based on so-called generator functions. Finally, symmetric distributions have their precise meaning: such a distribution is unchanged when, in the continuous case, its probability density function is reflected around a vertical line at some value of the random variable represented by the distribution. Whereas Archimedean copulas posses a kind of symmetry following from their exchangeability, they do not belong to symmetric distributions.

To investigate the limits of ChatGPT’s knowledge, let us prompt it with two further questions. According to the previous response, we can speculate that it has limited knowledge on the Clayton models with negative dependence.

We prompted ChatGPT to answer the same question three times and got contradicting answers. The first answer is correct, however, after asking again, ChatGPT changed its mind. Before commenting on that, let us try once again, with a bit more complex concept.

If (U1, U2) ∼ C, then the survival copula of C is the distribution of (1 − U1, 1 − U2), and thus the properties of the lower tail of C are the properties of the upper tail of the survival copula. Hence, we got an incorrect answer. After asking again, we got this response.

Again, we got contradicting answers. Based on this observation, the reader could raise the following question.

This response confirms what we have seen so far, hence, any user should take these limitations into account with the utmost seriousness and be extremely careful when asking ChatGPT for some reasoning. The examples above also well illustrate that the current version of ChatGPT is definitely not an appropriate tool for reasoning, which is as also observed by Frieder et al. (2023) and Bang et al. (2023). However, this by no means implies that it cannot serve as a helpful AI partner for pair programming.