I have a doubt about what type of prior to use for time. For example, I am trying to estimate the time in a port. I collected a bunch of data that measures time for a ship to stay in a port, but I do not have such data (eg. historical time in the port). In that case, can I use uninformative prior (eg. uniform distribution with - and 1) for the prior? But I know the ship does not stay in a port forever, in this case, what type of distribution should I use? Thanks alot!

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    $\begingroup$ If you don't want to use an improper prior, you can always use one such as a Uniform prior over $(0, 14)$ days, or some other arbitrarily large number of days as an upper bound. Freighters typically are in a port only 1-2 days, with long stays occurring largely to dock worker strikes, so if you want a prior on the mean number of days in port I'd probably use a Uniform(0,3) days. $\endgroup$ – jbowman Jan 14 at 4:55
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    $\begingroup$ That would imply they can never stay beyond the upper end of the uniform distribution, something that puts most of the probability mass in a plausible region and allows for a rare tail end (strikes, bancruptcy etc.) would seem more logical. You probably know that stays below some time are physically impossible (1s docking, anyone?). $\endgroup$ – Björn Jan 14 at 6:48
  • $\begingroup$ An improper prior is not a probability distribution, so cannot be interpreted as such. The positive mass on all possible integers in a uniform prior is not a statement that infinite values are possible. However, I would advise for a $1/n$ prior as this is more of a scale invariant problem, as you would like the same or a similar answer whether the stay is expressed in weeks, days, hours. $\endgroup$ – Xi'an Jan 14 at 6:54
  • $\begingroup$ What distribution for likelihood? Can you characterize your 'bunch of data"? $\endgroup$ – BruceET Jan 14 at 8:30

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