Description Usage Arguments Value References See Also Examples
View source: R/Gaussian_Inference.r
Generate the the density value of 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 density is p(x|m,S,A,b,Sigma).
1 2 | ## S3 method for class 'LinearGaussianGaussian'
dPosteriorPredictive(obj, x, A, b = NULL, LOG = TRUE, ...)
|
obj |
A "LinearGaussianGaussian" object. |
x |
matrix, or the ones that can be converted to matrix. Each row of x is an observation. |
A |
matrix or list. when x is a N x 1 matrix, A must be a matrix of N x dimz, dimz is the dimension of z; When x is 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 x is a N x 1 matrix, b must also be a N x 1 matrix or length N vector; When x is 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. |
LOG |
Return the log density if set to "TRUE". |
... |
Additional arguments to be passed to other inherited types. |
A numeric vector of the same length as nrow(x), the posterior predictive density.
Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.
LinearGaussianGaussian
, rPosteriorPredictive.LinearGaussianGaussian
, marginalLikelihood.LinearGaussianGaussian
1 2 3 4 5 6 |
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