rPosteriorPredictive.LinearGaussianGaussian: Generate random samples from the posterior predictive distribution of a "LinearGaussianGaussian" object

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

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

Arguments

obj

A "LinearGaussianGaussian" object.

integer, number of samples.

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.

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.

Examples

Run this code

# NOT RUN {
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)
# }