rPosterior: Generate random samples from the posterior distribution

Description

This is a generic function that will generate random samples from the posterior distribution. i.e. for the model structure: $$theta|gamma \sim H(gamma)$$ $$x|theta \sim F(theta)$$ generate random sampels of theta from the distribution $theta \sim H(gamma)$. For a given Bayesian bricks object obj, rPosterior() will generate random samples for different model structures:

class(obj)="LinearGaussianGaussian"

Where $$x \sim Gaussian(A z + b, Sigma)$$ $$z \sim Gaussian(m,S)$$ rPosterior() will generate random samples from Gaussian(m,S) See ?rPosterior.LinearGaussianGaussian for details.

class(obj)="GaussianGaussian"

Where $$x \sim Gaussian(mu,Sigma)$$ $$mu \sim Gaussian(m,S)$$ Sigma is known. rPosterior() will generate random samples from Gaussian(m,S) See ?rPosterior.GaussianGaussian for details.

class(obj)="GaussianInvWishart"

Where $$x \sim Gaussian(mu,Sigma)$$ $$Sigma \sim InvWishart(v,S)$$ mu is known. rPosterior() will generate random samples from InvWishart(v,S) See ?rPosterior.GaussianInvWishart for details.

class(obj)="GaussianNIW"

Where $$x \sim Gaussian(mu,Sigma)$$ $$Sigma \sim InvWishart(v,S)$$ $$mu \sim Gaussian(m,Sigma/k)$$ rPosterior() will generate random samples from NIW(m,k,v,S) See ?rPosterior.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. rPosterior() will generate random samples from NIG(m,V,a,b) See ?rPosterior.GaussianNIG for details.

class(obj)="CatDirichlet"

Where $$x \sim Categorical(pi)$$ $$pi \sim Dirichlet(alpha)$$ rPosterior() will generate random samples from Dirichlet(alpha) See ?rPosterior.CatDirichlet for details.

Usage

rPosterior(obj, ...)

Arguments

obj

A "BayesianBrick" object used to select a method.

...

further arguments passed to or from other methods.

Value

numeric, the density value