For the model 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.
Update the prior knowledge by adding the information of newly observed samples u, z and k. The model structure and prior parameters are stored in a "CatHDP2" object, the prior parameters in this object will be updated after running this function.
# S3 method for CatHDP2
posterior(obj, ss1, ss2, ss3, m, j, w = NULL, ...)A "CatHDP2" object.
Sufficient statistics of u. In CatHDP2 case the sufficient statistic of sample u is u itself(if u is a integer vector with all positive values).
Sufficient statistics of k. In CatHDP2 case the sufficient statistic of sample k is k itself(if k is a integer vector with all positive values).
Sufficient statistics of z. In CatHDP2 case the sufficient statistic of sample z is z itself(if z is a integer vector with all positive values).
integer, group label.
integer, subgroup label.
Sample weights, default NULL.
Additional arguments to be passed to other inherited types.
None. the model stored in "obj" will be updated based on "ss1" and "ss2".
Teh, Yee W., et al. "Sharing clusters among related groups: Hierarchical Dirichlet processes." Advances in neural information processing systems. 2005.