bf.dist.multivariate_student_t: Multivariate Student's t Distribution

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

Multivariate Student's t Distribution

Description

The Multivariate Student's t distribution is a generalization of the Student's t distribution to multiple dimensions. It is a heavy-tailed distribution that is often used to model data that is not normally distributed. The PDF of the multivariate Student's t-distribution for a random vector

x \in R^d

is given by:

f(x) = \frac{\Gamma\left(\frac{\nu + d}{2}\right)}{\Gamma\left(\frac{\nu}{2}\right) \nu^{d/2} \pi^{d/2} | \Sigma|^{1/2}} \left(1 + \frac{1}{\nu} (x - \mu)^T \Sigma^{-1} (x - \mu)\right)^{-(\nu + d)/2}

where: *

\Gamma(\cdot)

is the Gamma function. *

\mu

is the mean vector. *

\Sigma

is the scale (covariance) matrix. *

\nu

is the degrees of freedom. *

d

is the dimensionality of

\mathbf{x}

.

Usage

bf.dist.multivariate_student_t(
  df,
  loc = 0,
  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

df	A numeric vector representing degrees of freedom, must be positive.
loc	A numeric vector representing the location vector (mean) of the distribution.
scale_tril	A numeric matrix defining the scale (lower triangular 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. Optional boolean 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. When ‘sample=False' (model building), this is used with '.expand(shape)' 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 Multivariate Student's t distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the Multivariate Student's t distribution (for direct sampling).

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

See Also

https://num.pyro.ai/en/stable/distributions.html#multivariatestudentt

Examples

library(BayesForge)
m=importBF(platform='cpu')
bf.dist.multivariate_student_t(
df = 2,
loc =  c(1.0, 0.0, -2.0),
scale_tril = chol(
matrix(c( 2.0,  0.7, -0.3, 0.7,  1.0,  0.5, -0.3,  0.5,  1.5),
nrow = 3, byrow = TRUE)),
sample = TRUE)

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