bayesian inference -- multinomial likelihood with unknown number of categories.

Question

It is simple to do the Bayesian inference using a Multinomial likelihood with an Dirichlet conjugate prior. However, what if the $k$ categories in the multinomial likelihood is unknown, and the number of $k$ is changing (increasing in my case..) depends on new oberservations.

I guess there must be some papers doing this kind of inference, any suggestions? Thanks.

Answer 1

I found this paper answers the question well:

https://www.sciencedirect.com/science/article/pii/S0888613X04001069