Examples of how to generate informative priors?

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I have been trying to find some worked examples on how to make priors informative. I am using the ‘brms’ package in R to build linear models to evaluate the relationship between environmental variables and age or sex proportions. My main obstacle is to translate values that come from previous knowledge into the values that represent the parameters of a prior distribution. I have seen great examples but it is still hard for me to grasp.

I found a useful resource in this website: Developing informative priors • WILD6900

In that example the priors are for the probability of survival based on a Bernoulli distribution (which has one parameter, p). The recommended distribution for the prior in a Bayesian framework analysis is the Beta distribution because it can take values between 0 and 1.

The example illustrated how if you had prior “domain knowledge” of the mean survival of an organism (mu =0.9) and assume a variance of 0.005, through a formula you can assign the values to the parameters of the Beta distribution. The formulas for the alpha and beta parameters of Beta were:

alpha = ((1-mu/var) - 1/mu)mu^2 = 15.3
beta = alpha((1/mu) - 1) =1.7

The above allows for the prior probability of survival to highlight values of 0.8-0.9 and these values align themselves more with the expected survival of the organism than a uniform prior from 0-1.

Now here are my questions:

  1. Can I use the same logic to give informative priors to an intercept if my response variable is age/sex proportion since it is also a variable that ranges within 0 and 1?

  2. How would I do the same for a response variable like weight where the prior distribution would be Gamma or Normal?

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For discussion of “containment” prior models that suppress model configurations outside of a fixed interval in unconstrained, positively constrained, and interval constrained spaces see for example Prior Modeling.

On positively constrained and interval constrained spaces the difficulty is usually working out how to transform tail quantile conditions to prior density parameters. I discuss how to this in Stan in Some Ruminations on Containment Prior Modeling, and then demonstrate it for a variety of containment prior modeling approaches. For an example with a beta prior density see Towards A Principled Bayesian Workflow.

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Thank you for sharing, I have started reading these materials.

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