MPE: Get the Mean Posterior Estimate(MPE) of a "BayesianBrick"...

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

Description

This is a generic function that will generate the MPE estimate of a given "BayesianBrick" object. i.e. for the model structure:

theta|gamma \sim H(gamma)

x|theta \sim F(theta)

MPE estimate of theta is theta_MPE = E(theta|gamma,x), E() is the expectation function. For a given Bayesian bricks object obj, the MPE estimate will be:

class(obj)="LinearGaussianGaussian"

Where

x \sim Gaussian(A z + b, Sigma)

z \sim Gaussian(m,S)

MPE() will return the MPE estimate of z. See ?MPE.LinearGaussianGaussian for details.

class(obj)="GaussianGaussian"

Where

x \sim Gaussian(mu,Sigma)

mu \sim Gaussian(m,S)

Sigma is known. MPE() will return the MPE estimate of mu. See ?MPE.GaussianGaussian for details.

class(obj)="GaussianInvWishart"

Where

x \sim Gaussian(mu,Sigma)

Sigma \sim InvWishart(v,S)

mu is known. MPE() will return the MPE estimate of Sigma. See ?MPE.GaussianInvWishart for details.

class(obj)="GaussianNIW"

Where

x \sim Gaussian(mu,Sigma)

Sigma \sim InvWishart(v,S)

mu \sim Gaussian(m,Sigma/k)

MPE() will return the MPE estimate of mu and Sigma. See ?MPE.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. MPE() will return the MPE estimate of beta and sigma^2. See ?MPE.GaussianNIG for details.

class(obj)="CatDirichlet"

Where

x \sim Categorical(pi)

pi \sim Dirichlet(alpha)

MPE() will return the MPE estimate of pi. See ?MPE.CatDirichlet for details.

class(obj)="CatDP"

Where

x \sim Categorical(pi)

pi \sim DirichletProcess(alpha)

MPE() will return the MPE estimate of pi. See ?MPE.CatDP for details.

Usage

MPE(obj, ...)

Arguments

obj	A "BayesianBrick" object used to select a method.
...	further arguments passed to or from other methods.

Value

A list of MPE estimates

See Also

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

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