Priors

Definition

What is your best guesstimate of the parameter? Appears in the Bayes formula.

Which priors to pick?

1. There really is no prior information:
   a. Uniform Distribution is uninformative priors. However, it can be an illusion of being truly uninformative.
   b. I think there are Bayesian practioners who don’t look kindly on uniform distribution

2. Parameter’s range is from 0 to 1 (proportion)
   a. Beta Distribution

Parameter’s range must be positive and right-skewed

2. Gamma Distribution

Random effect in mixed-effect model.

1. Exponential Distribution

Conjugate priors

Conjugate Prior are prior probability distributions, when combined with a specific likehood function, produces a posterior distribution of the same probability distribution as the prior.