# posteriorDiscard.HDP: Update a "HDP" 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}

theta_k|psi \sim H0(psi)

x|theta_k,k \sim F(theta_k)

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. The choice of F() and H0() can be described by an arbitrary "BasicBayesian" object such as "GaussianGaussian","GaussianInvWishart","GaussianNIW", "GaussianNIG", "CatDirichlet", and "CatDP". See `?BasicBayesian` for definition of "BasicBayesian" objects, and see for example `?GaussianGaussian` for specific "BasicBayesian" instances. As a summary, An "HDP" object is simply a combination of a "CatHDP" object (see `?CatHDP`) and an object of any "BasicBayesian" type.
In the case of HDP, z and k can only be positive integers.
Contrary to posterior(), this function will update the prior knowledge by removing the information of observed samples x. The model structure and prior parameters are stored in a "CatDP" object, the prior parameters in this object will be updated after running this function.

## Usage

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

## Arguments

 `obj` A "HDP" object. `ss` Sufficient statistics of x of the "BasicBayesian" object, must be a list of sufficient statistics for each of the observations. Use sufficientStatistics(...,foreach=TRUE) to generate ss. `ss1` Sufficient statistics of k. In HDP 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 HDP 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.

`HDP`,`posteriorDiscard.HDP`,`sufficientStatistics.HDP`