bf.dist.student_t: Student's t-distribution.

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

Student's t-distribution.

Description

The Student's t-distribution is a probability distribution that arises in hypothesis testing involving the mean of a normally distributed population when the population standard deviation is unknown. It is similar to the normal distribution, but has heavier tails, making it more robust to outliers. For large

\nu

, it converges to the Normal distribution.

X \sim t_\nu(\mu, \sigma)

where:

*

\mu

is the **location (mean)** parameter *

\sigma > 0

is the **scale** parameter *

\nu > 0

is the **degrees of freedom** controlling the tail heaviness

Usage

bf.dist.student_t(
  df,
  loc = 0,
  scale = 1,
  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 parameter, defaults to 0.0.
scale	A numeric vector representing the scale parameter, defaults to 1.0.
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 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	Integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
create_obj	Logical. If 'TRUE', returns the raw BI distribution object instead of creating a sample site. This is essential for building complex distributions like 'MixtureSameFamily'.
to_jax	Boolean. Indicates whether to return a JAX array or not.

Value

- When sample=FALSE, a BI Student's t-distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the 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#studentt

Examples

library(BayesForge)
m=importBF(platform='cpu')
bf.dist.student_t(df = 2, loc = 0, scale = 2, sample = TRUE)

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