Characterizing Dirichlet Priors

The selection of prior distributions is a problem that has been heavily discussed since Bayes and Price published their article in 1763. Conjugate priors became popular, largely because of their mathematical convenience. In this study, we justify the use of the conjugate combination of a Dirichlet prior and a multinomial likelihood by imposing a fundamental principle that we call partition invariance, alongside other requirements that are well known in the literature.