bf.dist.matrix_normal: Matrix Normal Distribution

In BayesForge: Bayesian Inference using 'numpyro' and 'XLA'

Matrix Normal Distribution

Description

Samples from a Matrix Normal distribution, which is a multivariate normal distribution over matrices. The distribution is characterized by a location matrix and two lower triangular matrices that define the correlation structure. The distribution is related to the multivariate normal distribution in the following way. If

X \sim MN(loc,U,V) \implies vec(X) \sim MVN(vec(loc), kron(V,U) )

.

Usage

bf.dist.matrix_normal(
  loc,
  scale_tril_row,
  scale_tril_column,
  validate_args = py_none(),
  name = "x",
  obs = py_none(),
  mask = py_none(),
  sample = FALSE,
  seed = py_none(),
  shape = c(),
  event = 0,
  create_obj = FALSE,
  to_jax = TRUE
)

Arguments

loc	A numeric vector, matrix, or array representing the location of the distribution.
scale_tril_row	A numeric vector, matrix, or array representing the lower cholesky of rows correlation matrix.
scale_tril_column	A numeric vector, matrix, or array representing the lower cholesky of columns correlation matrix.
validate_args	Logical: Whether to validate parameter values. Defaults to 'reticulate::py_none()'.
name	A character string representing the name of the random variable within a model. This is used to uniquely identify the variable. Defaults to 'x'.
obs	A numeric vector or array of observed values. If provided, the random variable is conditioned on these values. If 'NULL', the variable is treated as a latent (unobserved) variable. Defaults to 'NULL'.
mask	A logical vector, matrix, or array (.BF_env$jnp$array) to mask observations.
sample	A logical value that controls the function's behavior. If 'TRUE', the function will directly draw samples from the distribution. If 'FALSE', it will create a random variable within a model. Defaults to 'FALSE'.
seed	An integer used to set the random seed for reproducibility when 'sample = TRUE'. This argument has no effect when 'sample = FALSE', as randomness is handled by the model's inference engine. Defaults to 0.
shape	A numeric vector specifying the shape of the distribution. Must be a vector.
event	An integer representing the number of batch dimensions to reinterpret as event dimensions.
create_obj	A logical value. If 'TRUE', returns the raw BI distribution object instead of creating a sample site.
to_jax	Boolean. Indicates whether to return a JAX array or not.

Value

- When sample=FALSE, a BI Matrix Normal distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the Matrix Normal distribution (for direct sampling).

- When create_obj=TRUE, the raw BI distribution object (for advanced use cases).

See Also

This is a wrapper of https://num.pyro.ai/en/stable/distributions.html#matrixnormal_lowercase

Examples

library(BayesForge)
m <- importBF(platform = "cpu")
n_rows <- 3
n_cols <- 4
loc <- matrix(rep(0, n_rows * n_cols), nrow = n_rows, ncol = n_cols, byrow = TRUE)

U_row_cov <-
  matrix(c(1.0, 0.5, 0.2, 0.5, 1.0, 0.3, 0.2, 0.3, 1.0),
    nrow = n_rows, ncol = n_rows, byrow = TRUE
  )
scale_tril_row <- chol(U_row_cov)

V_col_cov <- matrix(
  c(
    2.0, -0.8, 0.1, 0.4, -0.8, 2.0, 0.2, -0.2, 0.1,
    0.2, 2.0, 0.0, 0.4, -0.2, 0.0, 2.0
  ),
  nrow = n_cols, ncol = n_cols, byrow = TRUE
)
scale_tril_column <- chol(V_col_cov)


bf.dist.matrix_normal(
  loc = loc,
  scale_tril_row = scale_tril_row,
  scale_tril_column = scale_tril_column,
  sample = TRUE
)

BayesForge documentation built on June 9, 2026, 1:09 a.m.