bf.dist.wishart_cholesky: Wishart Cholesky Distribution

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

Wishart Cholesky Distribution

Description

* The **Wishart** distribution is a distribution over positive definite matrices, often used as a prior for covariance or precision matrices in multivariate normal models. * The **Cholesky parameterization** of the Wishart (called "wishart_cholesky" in Stan, for example) reparameterizes the Wishart over its **lower (or upper) triangular Cholesky factor**. This is useful for numerical stability and unconstrained parameterization in Bayesian sampling frameworks. * In this parameterization, one works with a lower-triangular matrix $L_W$ such that

\Sigma = L_W L_W^\top

and imposes a density over $L_W$ corresponding to the induced Wishart density on

\Sigma

.

The Wishart distribution is a multivariate distribution used as a prior distribution for covariance matrices. This implementation represents the distribution in terms of its Cholesky decomposition.

Usage

bf.dist.wishart_cholesky(
  concentration,
  scale_matrix = py_none(),
  rate_matrix = py_none(),
  scale_tril = py_none(),
  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

concentration	(numeric or vector) Positive concentration parameter analogous to the concentration of a 'Gamma' distribution. The concentration must be larger than the dimensionality of the scale matrix.
scale_matrix	(numeric vector, matrix, or array, optional) Scale matrix analogous to the inverse rate of a 'Gamma' distribution. If not provided, 'rate_matrix' or 'scale_tril' must be.
rate_matrix	(numeric vector, matrix, or array, optional) Rate matrix anaologous to the rate of a 'Gamma' distribution. If not provided, 'scale_matrix' or 'scale_tril' must be.
scale_tril	(numeric vector, matrix, or array, optional) Cholesky decomposition of the 'scale_matrix'. If not provided, 'scale_matrix' or 'rate_matrix' must be.
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	An optional boolean vector 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. This is used with ‘.expand(shape)' when 'sample=False' (model building) to set the distribution’s batch shape. When 'sample=True' (direct sampling), this is used as 'sample_shape' to draw a raw JAX array of the given shape.
event	An integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
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 Wishart Cholesky distribution object (for model building).

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

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

Examples

library(BayesForge)
m=importBF(platform='cpu')
bf.dist.wishart_cholesky(
concentration = 5,
scale_matrix = matrix(c(1,0,0,1),
nrow = 2),
sample = TRUE)

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