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I am new to Bayesian statistics, and would appreciate help understanding the Prior.

I want to combine a small national dataset with a prior from very large international studies, to give a posterior for the chance of success nationally.

I am using a prior from large international studies (thousands of observations) that point to 20% chance of success. I want to use this information in a beta-distributed prior, but how can I choose between for example (a=2 & b=8) and (a=20 & b=80)? Both represent a 20% success-rate, but will give the prior different "weight" on the posterior result, since the latter is a lot "surer" about the 20%-rate, right?

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  • $\begingroup$ If your international studies give mean success rates by country, I would have thought that a prior which came close to the unweighted mean and variance of the by-country distribution (erring on the side of a wider prior if you want to force it be a conjugate Beta prior) might be a possible approach. You might want to see whether the numbers are different by types of country and whether you should just use data from those like the country you are particularly interested in. $\endgroup$
    – Henry
    Commented Jun 28, 2021 at 22:42
  • $\begingroup$ I think this is the way forward, thanks! $\endgroup$
    – Johan
    Commented Jun 30, 2021 at 4:43

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Interpretation of $\alpha, \beta$ are the counts for success and failure respectively. They are not probabilities. See A Tutorial on Thompson Sampling. To provide a prior to updates, one needs to set up conjugate prior relations first, see Table of conjugate priors.

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  • $\begingroup$ I understand that alpha and beta in the posterior should be interpreted as the number of successes/failures in my own observation, but my understanding was that this is not the case for the prior. As my prior is based on international data with thousand of observations that would make the a and b in the Beta-distributed prior huge. In this (willhipson.netlify.app/post/bayesian_intro/binomial_gold) introduction, the example prior Beta-distribution is said to be a=2 and b=8, based on "rumours" that 20% of the land has gold in it, not based on 2, respecitvely 8, observations. $\endgroup$
    – Johan
    Commented Jun 27, 2021 at 9:36
  • $\begingroup$ Not sure how do you do updates. But check the paper linked in the answer, one would need to update likelihood over a dataset, it isn't given in one go. Start with alpha, beta very low, like 1-2 and see how large it updates over your dataset. Not all 1000s of observations would update alpha and beta. $\endgroup$ Commented Jun 27, 2021 at 16:55

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