dPosteriorPredictive.CatHDP2: Posterior predictive density function of a "CatHDP" object

In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

Description

Generate the the density value of the posterior predictive distribution of the following 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.
The model structure and prior parameters are stored in a "CatHDP" object.
Posterior predictive density = p(u,z,k|alpha,gamm,eta,U).

Usage

## S3 method for class 'CatHDP2'
dPosteriorPredictive(obj, u, k, z, m, j, LOG = TRUE, ...)

Arguments

obj	A "CatHDP" object.
u	integer, the elements of the vector must all greater than 0, the samples of a Categorical distribution.
k	integer, the elements of the vector must all greater than 0, the samples of a Categorical distribution.
z	integer, the elements of the vector must all greater than 0, the samples of a Categorical distribution.
m	integer, group label.
j	integer, subgroup label.
LOG	Return the log density if set to "TRUE".
...	Additional arguments to be passed to other inherited types.

Value

A numeric vector, the posterior predictive density.

References

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

See Also

CatHDP, dPosteriorPredictive.CatHDP

bbricks documentation built on July 8, 2020, 7:29 p.m.