Generate random samples from the posterior predictive distribution of the following structure:
$$G |eta \sim DP(eta,U)$$
$$G_m|gamma \sim DP(gamma,G), m = 1:M$$
$$pi_{mj}|G_m,alpha \sim DP(alpha,G_m), j = 1:J_m$$
$$z|pi_{mj} \sim Categorical(pi_{mj})$$
$$k|z,G_m \sim Categorical(G_m), \textrm{ if z is a sample from the base measure }G_m$$
$$u|k,G \sim Categorical(G), \textrm{ if k is a sample from the base measure G}$$
where DP(eta,U) is a Dirichlet Process on positive integers, eta is the "concentration parameter", U is the "base measure" of this Dirichlet process, U is an uniform distribution on all positive integers. DP(gamma,G) is a Dirichlet Process on integers with concentration parameter gamma and base measure G. DP(alpha,G_m) is a Dirichlet Process on integers with concentration parameter alpha and base measure G_m. Categorical() is the Categorical distribution. See dCategorical for the definition of the Categorical distribution.
In the case of CatHDP2, u, z and k can only be positive integers.
The model structure and prior parameters are stored in a "CatHDP2" object.
Posterior predictive is a distribution of u,z,k|alpha,gamm,eta,U.
# S3 method for CatHDP2
rPosteriorPredictive(obj, n = 1L, m, j, ...)A "CatHDP2" object.
integer, number of samples.
integer, group label.
integer, subgroup label.
Additional arguments to be passed to other inherited types.
integer, the categorical samples.
Teh, Yee W., et al. "Sharing clusters among related groups: Hierarchical Dirichlet processes." Advances in neural information processing systems. 2005.