So what did we learn from all of this? Well hopefully you learned that setting priors is not something you learn over-night. It takes practice to get a feel for it. However, the principles are exceedingly obvious. I will leave you with some hard core advice on how to set priors.
- Always set the priors in the vicinity of what you believe the truth is
- Always set the priors such that they reflect the same order of magnitude as the phenomenon you’re trying to predict
- Don’t be overconfident, leave space for doubt
- Never use completely uninformative priors
- Whenever possible refrain from using uniform distributions
- Always sum up the consequence of all of your priors such that if no data was available your model still predicts in the same order of magnitude as your observed response
- Be careful, and be honest! Never postulate very informative priors on results you WANT to be true. It’s OK if you BELIEVE them to be true. Don’t rest your mind until you see the difference.