As a young man Mr Gott visits Berlin in 1969. He’s surprised that he cannot cross into East Berlin since there is a wall separating the two halves of the city. He’s told that the wall was erected 8 years previously. He reasons that : The wall will have a finite lifespan; his ignorance means that he arrives uniformly at random at some time in the lifespan of the wall. Since only 5% of the time one would arrive in the first or last 2.5% of the lifespan of the wall he asserts that with 95% confidence the wall will survive between 8/0.975 ≈ 8.2 and 8/0.025 = 320 years. In 1989 the now Professor Gott is pleased to find that his prediction was correct and promotes his prediction method in elite journals. This ‘delta-t’ method is widely adopted and used to form predictions in a range of scenarios about which researchers are ‘totally ignorant’. Would you ‘buy’ a prediction from Prof. Gott? Explain carefully your reasoning.

My answer to this question is no, I would not buy a prediction from Prof. Gott as his "confidence interval" is very large and hence it was not too accurate. But how exactly would one go about explaining this more rigourously?

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    $\begingroup$ The most dubious thing in my opinion is that there is only one sampling unit in the sample. $\endgroup$ Commented Aug 11, 2021 at 9:33
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    $\begingroup$ this is the infamous "doomsday argument", and I believe involves a delicate analysis of likelihood versus probability. You can read up on it, but it is similar to the German tanks problem, and I don't think it has been really resolved. $\endgroup$
    – user619894
    Commented Aug 11, 2021 at 9:51


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