| >> Can it come up with...when it has no idea that such a concept exists? > I was curious to see if it could. But you told it about the concept, "a new statistic that mixes hessian and likelihood with score". You should try a different experiment. I'm more familiar with architecture than statistics so I'll use the floor plan example. Were someone in 16th century had asked its LLM to address the painpoints of the joined room approach, and then the LLM conceived of the novell concept of a corridor. [Look up the origin of the word.] If that 16th century LLM spat out "the overall concept is to distinguish between transient and in repose spaces. There is already something similar in military architecture called 'corridor', which is a strip of land along the outer edge of a ditch. In these new floor plan designs, there will be corridors internal and peripheral to the building that will connect rooms, just like corridors (strips of land) connect lots or permit movement without stepping into a ditch". -- can this happen? -- You: Invent a novel test statistic that can be used to test hypotheses about the parameters of the model, such as whether they are equal to a particular value or whether they differ across groups or conditions. You can combine existing statistical tools. gpt: How about "Hessian-score likelihood ratio"? The idea behind this concept is to use the Hessian matrix, which captures second-order information about the likelihood function, along with the score function, which measures the sensitivity of the likelihood function to changes in the model parameters, to construct a likelihood ratio test statistic. |