# rPosteriorPredictive.LinearGaussianGaussian: Generate random samples from the posterior predictive... In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

## Description

Generate random samples from the posterior predictive distribution of the following structure:

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

z \sim Gaussian(m,S)

Where Sigma is known. A is a dimx x dimz matrix, x is a dimx x 1 random vector, z is a dimz x 1 random vector, b is a dimm x 1 vector. Gaussian() is the Gaussian distribution. See `?dGaussian` for the definition of Gaussian distribution.
The model structure and prior parameters are stored in a "LinearGaussianGaussian" object.
Posterior predictive is a distribution of x|m,S,A,b,Sigma.

## Usage

 ```1 2``` ```## S3 method for class 'LinearGaussianGaussian' rPosteriorPredictive(obj, n = 1, A, b = NULL, ...) ```

## Arguments

 `obj` A "LinearGaussianGaussian" object. `n` integer, number of samples. `A` matrix or list. when you want the random samples x to be a n x 1 matrix, A must be a matrix of n x dimz, dimz is the dimension of z; When you want the random samples x to be a N x dimx matrix, where dimx > 1, A can be either a list or a matrix. When A is a list, A = {A_1,A_2,...A_N} is a list of dimx x dimz matrices. If A is a single dimx x dimz matrix, it will be replicated N times into a length N list. `b` matrix, when you want the random samples x to be a N x 1 matrix, b must also be a N x 1 matrix or length N vector; When you want x to be a N x dimx matrix, where dimx > 1, b can be either a matrix or a vector. When b is a matrix, b={b_1^T,...,b_N^T} is a N x dimx matrix, each row is a transposed vector. When b is a length dimx vector, it will be transposed into a row vector and replicated N times into a N x dimx matrix. When b = NULL, it will be treated as a vector of zeros. Default NULL. `...` Additional arguments to be passed to other inherited types.

## Value

A matrix of n rows, each row is a sample.

## References

Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.

`LinearGaussianGaussian`, `dPosteriorPredictive.LinearGaussianGaussian`

## Examples

 ```1 2 3 4 5``` ```obj <- LinearGaussianGaussian(gamma=list(Sigma=matrix(c(2,1,1,2),2,2), m=c(0.2,0.5,0.6),S=diag(3))) A <- matrix(runif(6),2,3) b <- runif(2) rPosteriorPredictive(obj = obj,n=20,A=A,b=b) ```

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