MAP: Get the Maximum A Posteriori(MAP) estimate of a "BayesianBrick" object

Description

This is a generic function that will generate the MAP estimate of a given "BayesianBrick" object. For the model structure: $$theta|gamma \sim H(gamma)$$ $$x|theta \sim F(theta)$$ MAP estimate of theta is theta_MAP = argmax_theta p(theta|gamma,x). For a given Bayesian bricks object obj, the MAP estimate will be:

class(obj)="LinearGaussianGaussian"

Where $$x \sim Gaussian(A z + b, Sigma)$$ $$z \sim Gaussian(m,S)$$ MAP() will return the MAP estimate of z. See ?MAP.LinearGaussianGaussian for details.

class(obj)="GaussianGaussian"

Where $$x \sim Gaussian(mu,Sigma)$$ $$mu \sim Gaussian(m,S)$$ Sigma is known. MAP() will return the MAP estimate of mu. See ?MAP.GaussianGaussian for details.

class(obj)="GaussianInvWishart"

Where $$x \sim Gaussian(mu,Sigma)$$ $$Sigma \sim InvWishart(v,S)$$ mu is known. MAP() will return the MAP estimate of Sigma. See ?MAP.GaussianInvWishart for details.

class(obj)="GaussianNIW"

Where $$x \sim Gaussian(mu,Sigma)$$ $$Sigma \sim InvWishart(v,S)$$ $$mu \sim Gaussian(m,Sigma/k)$$ MAP() will return the MAP estimate of mu and Sigma. See ?MAP.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. MAP() will return the MAP estimate of beta and sigma^2. See ?MAP.GaussianNIG for details.

class(obj)="CatDirichlet"

Where $$x \sim Categorical(pi)$$ $$pi \sim Dirichlet(alpha)$$ MAP() will return the MAP estimate of pi. See ?MAP.CatDirichlet for details.

class(obj)="CatDP"

Where $$x \sim Categorical(pi)$$ $$pi \sim DirichletProcess(alpha)$$ MAP() will return the MAP estimate of pi. See ?MAP.CatDP for details.

Usage

MAP(obj, ...)

Arguments

obj

A "BayesianBrick" object used to select a method.

...

further arguments passed to or from other methods.

Value

A list of the MAP estimates