dPosteriorPredictive.HDP {bbricks} | R Documentation |
Generate the the density value of the posterior predictive distribution of the following 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.
The model structure and prior parameters are stored in a "HDP" object.
Posterior predictive density = p(x,z,k|gamma,alpha,psi) when x is not NULL, or p(z,k|gamma,alpha,psi) when x is NULL.
## S3 method for class 'HDP' dPosteriorPredictive(obj, x = NULL, z, k, j, LOG = TRUE, ...)
obj |
A "HDP" object. |
x |
Random samples of the "BasicBayesian" object. |
z |
integer. |
k |
integer, the partition label of the parameter space where the observation x is drawn from. |
j |
integer, group label. |
LOG |
Return the log density if set to "TRUE". |
... |
Additional arguments to be passed to other inherited types. |
A numeric vector, the posterior predictive density.
Teh, Yee W., et al. "Sharing clusters among related groups: Hierarchical Dirichlet processes." Advances in neural information processing systems. 2005.
HDP
, dPosteriorPredictive.HDP
, marginalLikelihood.HDP