He did certain things, like went to a certain college, got married and had kids at particular ages, went to a certain type of grad school, took and quit certain jobs at certain times. I went through and asked, of each observation, the Bayesian question of whether the probability of that observation differed in the worlds where the hypothesis was true and false. In all 12 of my cases, where I was doing it by hand in an Excel spreadsheet using Bayes' Theorem in its probability form, I judged the observation was more likely in the world where he was indeed avoiding the Vietnam draft.
I started over with Gemini with the prompt "can you evaluate the final odds for a hypothesis, given a number of observations that could be evidence for or against that hypothesis". It first laid out Bayes' Theorem in its odds form, and then asked me to lay out the hypothesis and set of observations.
I did so, with it leading me through asking for three or four observations at a time. Gemini came up with its own assessment of the odds for each one, justifying the odds it gave based on historical background context like draft rules around going to college; worked up the running odds as it went; and provided a narrative interpretation.
Gemini's final tally of observations was 10 in favor, 2 neutral, and 2 against, where my own by-hand analysis in a spreadsheet had come out 12-0 in favor (Gemini came up with a couple more things like inquiring about his 1969 draft lottery number). The individual odds we came up with independently were largely quite comparable. Gemini's final aggregated odds were 124,000-to-1 in favor where my spreadsheet analysis had 4600-to-1. Its final narrative assessment was that the history I described appeared to be a classic case of "draft hedge."
He did certain things, like went to a certain college, got married and had kids at particular ages, went to a certain type of grad school, took and quit certain jobs at certain times. I went through and asked, of each observation, the Bayesian question of whether the probability of that observation differed in the worlds where the hypothesis was true and false. In all 12 of my cases, where I was doing it by hand in an Excel spreadsheet using Bayes' Theorem in its probability form, I judged the observation was more likely in the world where he was indeed avoiding the Vietnam draft.
I started over with Gemini with the prompt "can you evaluate the final odds for a hypothesis, given a number of observations that could be evidence for or against that hypothesis". It first laid out Bayes' Theorem in its odds form, and then asked me to lay out the hypothesis and set of observations.
I did so, with it leading me through asking for three or four observations at a time. Gemini came up with its own assessment of the odds for each one, justifying the odds it gave based on historical background context like draft rules around going to college; worked up the running odds as it went; and provided a narrative interpretation.
Gemini's final tally of observations was 10 in favor, 2 neutral, and 2 against, where my own by-hand analysis in a spreadsheet had come out 12-0 in favor (Gemini came up with a couple more things like inquiring about his 1969 draft lottery number). The individual odds we came up with independently were largely quite comparable. Gemini's final aggregated odds were 124,000-to-1 in favor where my spreadsheet analysis had 4600-to-1. Its final narrative assessment was that the history I described appeared to be a classic case of "draft hedge."