# Modeling the effect of a very erronous initial prior on Bayesian Inference

I am trying to get a grasp of the case that a very intuitive initial prior provided to a Bayesian Inference process turns out to be entirely wrong. Is there a standard model for the effect of error in an initial prior?

That might just get me more comfortable in picking an initial prior and choosing Bayesian Inference in the first place.

• Not really, unless you can embed your prior within a family of priors and run a hierarchical Bayes inference over that family. There are however some Bayesian approaches to prior misspecification as posterior predictive and Evans' relative belief. Mar 5 '16 at 20:42
• Frankly I have found web.stanford.edu/class/msande226/lecture16_inference.pdf equally as helpful in providing a good perspective as any of the answers here.
– matt
Mar 17 '16 at 20:03

Another common cause of unreasonable priors is because you lack an intuitive handle on what your model parameters mean. A strategy for dealing with that is to reparameterize in term of quantities that are more meaningful to your intuition. For example, a beta distribution is usually parameterized in terms of parameters $\alpha$ and $\beta$ that have no clear intuitive interpretation; reparameterizing in terms of the mean and standard deviation of the distribution makes it much easier to specify a reasonable prior.
• Actually, all conjugate priors have an interpretation as hypothetical historical data (e.g. for a beta as the prior for a binomial the interpretation is having observed historical prior information equivalent to $y=\alpha$ out of $n=\alpha+\beta$ successes). Mar 6 '16 at 6:40