rPosteriorPredictive: Generate random samples from the posterior predictive...

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

Description

This is a generic function that will generate random samples from the posterior predictive distribution. i.e. for the model structure:

theta|gamma \sim H(gamma)

x|theta \sim F(theta)

generate x_new from the posterior predictive distribution of x|gamma. For a given Bayesian bricks object obj, rPosteriorPredictive() will generate random samples from different model structures:

class(obj)="LinearGaussianGaussian"

Where

x \sim Gaussian(A z + b, Sigma)

z \sim Gaussian(m,S)

rPosteriorPredictive() will generate samples from the distribution of x|m,S,A,b,Sigma See ?rPosteriorPredictive.LinearGaussianGaussian for details.

class(obj)="GaussianGaussian"

Where

x \sim Gaussian(mu,Sigma)

mu \sim Gaussian(m,S)

Sigma is known. rPosteriorPredictive() will generate samples from the distribution of x|m,S,Sigma See ?rPosteriorPredictive.GaussianGaussian for details.

class(obj)="GaussianInvWishart"

Where

x \sim Gaussian(mu,Sigma)

Sigma \sim InvWishart(v,S)

mu is known. rPosteriorPredictive() will generate samples from the distribution of x|mu,v,S See ?rPosteriorPredictive.GaussianInvWishart for details.

class(obj)="GaussianNIW"

Where

x \sim Gaussian(mu,Sigma)

Sigma \sim InvWishart(v,S)

mu \sim Gaussian(m,Sigma/k)

rPosteriorPredictive() will generate samples from the distribution of x|m,k,v,S See ?rPosteriorPredictive.GaussianNIW for details.

class(obj)="GaussianNIG"

Where

x \sim Gaussian(X beta,sigma^2)

sigma^2 \sim InvGamma(a,b)

beta \sim Gaussian(m,sigma^2 V)

X is a row vector, or a design matrix where each row is an obervation. rPosteriorPredictive() will generate samples from the distribution of x,X|m,V,a,b See ?rPosteriorPredictive.GaussianNIG for details.

class(obj)="CatDirichlet"

Where

x \sim Categorical(pi)

pi \sim Dirichlet(alpha)

rPosteriorPredictive() will generate samples from the distribution of x|alpha See ?rPosteriorPredictive.CatDirichlet for details.

class(obj)="CatDP"

Where

x \sim Categorical(pi)

pi \sim DirichletProcess(alpha)

rPosteriorPredictive() will generate samples from the distribution of x|alpha See ?rPosteriorPredictive.CatDP for details.

Usage

rPosteriorPredictive(obj, n, ...)

Arguments

obj	A "BayesianBrick" object used to select a method.
n	integer, specify the number of samples to be generated.
...	further arguments passed to or from other methods.

Value

a matrix or vector or list of random samples, depends on the type of 'obj'.

See Also

rPosteriorPredictive.GaussianNIW for Gaussian-NIW conjugate structure, rPosteriorPredictive.GaussianNIG for Gaussian-NIG conjugate structure, rPosteriorPredictive.CatDirichlet for Categorical-Dirichlet conjugate structure, rPosteriorPredictive.CatDP for Categorical-DP conjugate structure ...

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