MAP: Get the Maximum A Posteriori(MAP) estimate of a...

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

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

See Also

MAP.LinearGaussianGaussian for Linear Gaussian and Gaussian conjugate structure, MAP.GaussianGaussian for Gaussian-Gaussian conjugate structure, MAP.GaussianInvWishart for Gaussian-Inverse-Wishart conjugate structure, MAP.GaussianNIW for Gaussian-NIW conjugate structure, MAP.GaussianNIG for Gaussian-NIG conjugate structure, MAP.CatDirichlet for Categorical-Dirichlet conjugate structure, MAP.CatDP for Categorical-DP conjugate structure ...

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