dPosteriorPredictive.HDP2 {bbricks} | R Documentation |
Generate the the density value of the posterior predictive distribution of the following 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 model structure and prior parameters are stored in a "HDP2" object.
Posterior predictive density = p(u,z,k,x|eta,gamma,alpha,psi) when x is not NULL, or p(u,z,k|eta,gamma,alpha,psi) when x is NULL.
## S3 method for class 'HDP2' dPosteriorPredictive(obj, x = NULL, u, k, z, m, j, LOG = TRUE, ...)
obj |
A "HDP2" object. |
x |
Random samples of the "BasicBayesian" object. |
u |
integer, the partition label of the parameter space where the observation x is drawn from. |
k |
integer. |
z |
integer. |
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. |
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.
HDP2
, dPosteriorPredictive.HDP2
, marginalLikelihood.HDP2