dPosterior: Get the density from the posterior distribution.

Description

This is a generic function that will generate the the density value of the posterior distribution. i.e. for the model structure: $$theta|gamma \sim H(gamma)$$ $$x|theta \sim F(theta)$$ get the probability density/mass from the distribution $theta \sim H(gamma)$. For a given Bayesian bricks object obj and an observation of theta, dPosterior() will calculate the density value for different model structures:

class(obj)="LinearGaussianGaussian"

Where $$x \sim Gaussian(A z + b, Sigma)$$ $$z \sim Gaussian(m,S)$$ dPosterior() will return p(theta|m,S) See ?dPosterior.LinearGaussianGaussian for details.

class(obj)="GaussianGaussian"

Where $$x \sim Gaussian(mu,Sigma)$$ $$mu \sim Gaussian(m,S)$$ Sigma is known. dPosterior() will return p(mu|m,S) See ?dPosterior.GaussianGaussian for details.

class(obj)="GaussianInvWishart"

Where $$x \sim Gaussian(mu,Sigma)$$ $$Sigma \sim InvWishart(v,S)$$ mu is known. dPosterior() will return p(Sigma|v,S) See ?dPosterior.GaussianInvWishart for details.

class(obj)="GaussianNIW"

Where $$x \sim Gaussian(mu,Sigma)$$ $$Sigma \sim InvWishart(v,S)$$ $$mu \sim Gaussian(m,Sigma/k)$$ dPosterior() will return p(mu,Sigma|m,k,v,S) See ?dPosterior.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. dPosterior() will return p(beta,sigma^2|m,V,a,b) See ?dPosterior.GaussianNIG for details.

class(obj)="CatDirichlet"

Where $$x \sim Categorical(pi)$$ $$pi \sim Dirichlet(alpha)$$ dPosterior() will return p(pi|alpha) See ?dPosterior.CatDirichlet for details.

Usage

dPosterior(obj, ...)

Arguments

obj

A "BayesianBrick" object used to select a method.

...

further arguments passed to or from other methods.

Value

numeric, the density value