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I have a dataset made up of the date (YYYYMMDD) of a specific event, with the time period spanning from 1970-2015.

I want to compare two time periods of 10 years each, and look at the yearly total number of events in both time periods. I'm doing a bayesian inference to determine the significance of the difference in terrorist events.

I figured that the prior would be the distributions across the entire dataset, regardless of year. Does that make sense?

Also, can anyone point me to good resources on how to pick distributions? I'm still learning bayesian statistics and don't quite understand when I'd pick an informative vs uninformative

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    $\begingroup$ It is hard to comment on priors without knowing anything about your model, or the data you have. $\endgroup$
    – Tim
    May 25, 2020 at 16:02

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In general there is no law what prior to select or how to select it. It remains a difficult question. There are three strategies: non-informative, conjugate and expert priors.

  • Non-Informative: If you have no prior knowledge the safest choice is literally the non-informative prior, e.g. the uniform distribution. The choice of a non-informational prior is well justified by the desire to reduce the subjective element as much as possible. Jeffrey's prior might be a valid choice as well.
  • Conjugate: Conjugate priors have the nice property that the resulting distribution of the posterior is from the same probability family as the prior. This has computational advantages since we can find analytic formulas and there is no need for computational costly methods to calculate the posterior. See Conjugate prior for some conjugate priors.
  • Expert: The last prior is one defined the one or several experts.

Note: The prior distribution should be defined before looking at the data. So in your case taking the distribution over the entire data set kinda defeats the Bayesian approach.

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