bf.dist.truncated_distribution: Truncated Distribution

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

Truncated Distribution

Description

A **truncated distribution** arises when you take a random variable

X

that originally has some distribution (with PDF

f_X(x)

and CDF

F_X(x)

) and you restrict attention only to those values of

X

that are *above* a given truncation point

a

. In other words you only observe $X$ when $X > a$. All the "mass" below (or equal to)

a

is **excluded** (not just unobserved, but removed from the sample/analysis). This differs from *censoring*, where values below a threshold might be known (for example "< a"), but here they are entirely excluded from the domain. Left truncation is common in many applied fields.

Usage

bf.dist.truncated_distribution(
  base_dist,
  low = py_none(),
  high = 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

base_dist	The base distribution to be truncated. This should be a univariate distribution. Currently, only the following distributions are supported: Cauchy, Laplace, Logistic, Normal, and StudentT.
low	(float, jnp.ndarray, optional): The lower truncation point. If 'None', the distribution is only truncated on the right. Defaults to 'None'.
high	(float, jnp.ndarray, optional): The upper truncation point. If 'None', the distribution is only truncated on the left. Defaults to 'None'.
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 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 (e.g., 'c(10)') specifying the shape. 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	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 Truncated distribution object (for model building).

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

Examples

library(BayesForge)
m=importBF(platform='cpu')
bf.dist.truncated_distribution(
base_dist = bf.dist.normal(0,1, create_obj = TRUE),
high = 0.7,
low = 0.1,
sample = TRUE)

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