A new prior distribution on the simplex: the extended flexible Dirichlet

The Dirichlet is a very popular prior distribution for the multinomial’s probability vector parameter, due to its simplicity. Nonetheless, the Dirichlet density function cannot model many reasonable shapes (i.e. multi-modalities and/or positive covariances). This work aims to perform a preliminary study of the extended flexible Dirichlet (EFD) as a possible prior distribution. In particular, we show that the EFD prior is conjugate to the multinomial scheme and explain how the hyper-parameters change once a sample is observed