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I'm on the hunt for an example to illustrate the difference between frequentist and subjective Bayesian probability. In particular, I'd like a type of event for which frequentist probability doesn't make sense.

This is the example I have: What is the probability that it will rain on March 14th, 2018 in London UK?

As far as I know, there can be no long-run relative frequency for this event. One could, of course, approximate this by asking "The probability it will rain on any March 14th in London UK", but as far as I can tell that is different.

Does this example make sense? Is there a better one?

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  • $\begingroup$ See stats.stackexchange.com/questions/332026/… $\endgroup$ Mar 12, 2018 at 21:50
  • $\begingroup$ Why do you think Bayesian applies here? Think about it for a moment. I can reject your Bayesian probability on the same exact grounds you rejected what you called frequentist forecast. $\endgroup$
    – Aksakal
    Mar 13, 2018 at 0:47
  • $\begingroup$ Perhaps something like "what is the probability that George Washington died in 1801?" This, give or take a little, is an example that I learned in a Foundations of Bayesian Statistics many, many years ago. You can certainly construct a bet on it, implying there's a subjective probability, but hard to see how you'd construct a frequentist probability out of a past event that is known to have happened / not happened, just not by you. $\endgroup$
    – jbowman
    Apr 7, 2018 at 21:14

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To me, the best illustrations of the differences are one-off events, where the concept of repeated sampling does not make sense. For example, the first time that humans fly to Mars, we might ask, "What is the probability that they will reach the planet?" It seems absurd to reframe the question by asking, "If we repeatedly flew to Mars for the first time, what proportion of missions would succeed?"

I'm just an applied statistician, so some theorist may find fault in my example; or find a reason why Bayesian analysis would not work either. Still, the example speaks to me.

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