posterior.HDP2 {bbricks} | R Documentation |

For the model structure:

*G |eta \sim DP(eta,U)*

*G_m|gamma,G \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_{mj}*

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

*theta_u|psi \sim H0(psi)*

*x|theta_u,u \sim F(theta_u)*

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. 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 "HDP2" object is simply a combination of a "CatHDP2" object (see `?CatHDP2`

) and an object of any "BasicBayesian" type.

In the case of HDP2, u, z and k can only be positive integers.

This function will update the prior knowledge by adding the information of newly observed samples x, z and k. The model structure and prior parameters are stored in a "HDP2" object, the prior parameters in this object will be updated after running this function.

## S3 method for class 'HDP2' posterior(obj, ss = NULL, ss1, ss2, ss3, m, j, w = NULL, ...)

`obj` |
A "HDP2" 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 u. In HDP2 case the sufficient statistic of sample u is u itself(if u is a integer vector with all positive values). |

`ss2` |
Sufficient statistics of k. In HDP2 case the sufficient statistic of sample k is k itself(if k is a integer vector with all positive values). |

`ss3` |
Sufficient statistics of z. In HDP2 case the sufficient statistic of sample z is z itself(if z is a integer vector with all positive values). |

`m` |
integer, group label. |

`j` |
integer, subgroup label. |

`w` |
Sample weights, default NULL. |

`...` |
Additional arguments to be passed to other inherited types. |

None. the model stored in "obj" will be updated based on "ss", "ss1", "ss2"and "ss3".

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

`HDP2`

,`posteriorDiscard.HDP2`

,`sufficientStatistics.HDP2`

[Package *bbricks* version 0.1.4 Index]