rPosteriorPredictive: Generate random samples from the posterior predictive distribution

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.

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'.