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I have data on 500 examinees with responses to 20 questions. Because the response is dichotomous, I use Beta(1,1) as the conjugate prior. Now I’m interested in using Beta(alpha, alpha) as the prior. How can I estimate alpha? I hope to do it in R.

Scortchi - Reinstate Monica
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Stephen Jung
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  • I tried to fix up your grammar so that it is more understandable, but perhaps I failed. What is your dependent variable? What are your independent variables? – Peter Flom Nov 28 '12 at 11:27

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If I've understood you right, you're trying to come up with parameters for the prior beta distribution of a binomial probability - often that's called elicitation rather than estimation.

Garthwaite, Kadane, & O'Hagan discuss this in 'Statistical Methods for Eliciting Probability Distributions' (JASA 2005). Obviously few people are familiar enough with probability distributions to be able to come up stright away with parameters that represent their beliefs. But you can think about (1) quantiles, (2) hypothetical future samples, (3) equivalent prior samples, or (4) relative values of probability density functions. The paper's worth reading.

Scortchi - Reinstate Monica
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