sufficientStatistics.HDP2 {bbricks} | R Documentation |

For following 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.

The sufficient statistics of a set of samples x in a "HDP2" object is the same sufficient statistics of the "BasicBayesian" inside the "HDP2", see examples.

## S3 method for class 'HDP2' sufficientStatistics(obj, x, ...)

`obj` |
A "HDP2" object. |

`x` |
Random samples of the "BasicBayesian" object. |

`...` |
further arguments passed to the corresponding sufficientStatistics method of the "BasicBayesian" object. |

Return the sufficient statistics of the corresponding BasicBayesian type, see examples.

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

`HDP2`

, `sufficientStatistics_Weighted.HDP2`

## a HDP2 with Gaussian NIW observations obj1 <- HDP2(gamma=list(gamma=1,alpha=1,j=2,m=2, H0aF="GaussianNIW", parH0=list(m=0,k=1,v=2,S=1))) ## a HDP2 with Categorical-Dirichlet observations obj2 <- HDP2(gamma=list(gamma=1,alpha=1,j=2,m=2, H0aF="CatDirichlet", parH0=list(alpha=1,uniqueLabels=letters[1:3]))) x1 <- rnorm(100) x2 <- sample(letters[1:3],100,replace = TRUE) sufficientStatistics(obj = obj1,x=x1,foreach = FALSE) sufficientStatistics(obj = obj2,x=x2,foreach = FALSE) sufficientStatistics(obj = obj1,x=x1,foreach = TRUE)

[Package *bbricks* version 0.1.4 Index]