I need a rather a prior on the parameters of a Beta distribution (i.e. $\alpha$ and $\beta$). I have an external constraint that requires me to use univariate priors, one for $\alpha$ and one $\beta$.

Ideally I would like to use two univariate priors that together are as close as possible to something like $p(\alpha,\beta)∝(\alpha+\beta)^{−5/2}$ (for anyone interested in this particular choice, see this thread)

What priors can I use for them?


1 Answer 1


Any prior on $\alpha$ (or $\beta$) is admissible as long as it satisfies the requirements of the beta distribution in your parameterization, usually $\alpha >0$ and $\beta >0$, and as long as it yields a finite posterior. Assuming univariate priors and independence of $\alpha$ and $\beta$, one option might be the exponential distribution, since it's bounded by $0$. Additionally, it has a mode at $0$, meaning that plausible values will tend to be small. Some might find this attractive because they may desire only vague prior information. In this case, your prior is $$p(\alpha)=\lambda_\alpha\exp(-\lambda_\alpha \alpha)$$$$p(\beta)=\lambda_\beta\exp(-\lambda_\beta \beta)$$

But this is just an example. Any non-negative prior is an option. Modern Bayesian inference software such as Stan dose not restrict you to conjugate priors.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.