# posterior.CatHDP: Update a "CatHDP" object with sample sufficient statistics In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

## Description

For the model structure:

G|gamma \sim DP(gamma,U)

pi_j|G,alpha \sim DP(alpha,G), j = 1:J

z|pi_j \sim Categorical(pi_j)

k|z,G \sim Categorical(G), \textrm{ if z is a sample from the base measure G}

where DP(gamma,U) is a Dirichlet Process on positive integers, gamma is the "concentration parameter", U is the "base measure" of this Dirichlet process, U is an uniform distribution on all positive integers. DP(alpha,G) is a Dirichlet Process on integers with concentration parameter alpha and base measure G. Categorical() is the Categorical distribution. See `dCategorical` for the definition of the Categorical distribution.
In the case of CatHDP, z and k can only be positive integers.
Update the prior knowledge by adding the information of newly observed samples z and k. The model structure and prior parameters are stored in a "CatHDP" object, the prior parameters in this object will be updated after running this function.

## Usage

 ```1 2``` ```## S3 method for class 'CatHDP' posterior(obj, ss1, ss2, j, w = NULL, ...) ```

## Arguments

 `obj` A "CatHDP" object. `ss1` Sufficient statistics of k. In CatHDP case the sufficient statistic of sample k is k itself(if k is a integer vector with all positive values). `ss2` Sufficient statistics of z. In CatHDP case the sufficient statistic of sample z is z itself(if z is a integer vector with all positive values). `j` integer, group label. `w` Sample weights, default NULL. `...` Additional arguments to be passed to other inherited types.

## Value

None. the model stored in "obj" will be updated based on "ss1" and "ss2".

## References

Teh, Yee W., et al. "Sharing clusters among related groups: Hierarchical Dirichlet processes." Advances in neural information processing systems. 2005.

`CatHDP`,`posteriorDiscard.CatHDP`