bf.dist.zero_inflated_negative_binomial: Zero-Inflated Negative Binomial Distribution

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

Zero-Inflated Negative Binomial Distribution

Description

A Zero-Inflated Negative Binomial distribution is used for count data that exhibit **both** (a) over-dispersion relative to a Poisson (i.e., variance > mean) *and* (b) an excess of zero counts beyond what a standard Negative Binomial would predict. It assumes two latent processes: 1. With probability

\pi

(sometimes denoted

\psi

or "zero-inflation probability") you are in a "structural zero" state ??? you observe a zero. 2. With probability

1 - \pi

, you come from a regular Negative Binomial distribution (with parameters e.g. mean

\mu

and dispersion parameter

\alpha

or size/r parameter) and then you might observe zero or a positive count. Thus the model is a mixture of a point-mass at zero + a Negative Binomial for counts. This distribution combines a Negative Binomial distribution with a binary gate variable. Observations are either drawn from the Negative Binomial distribution with probability (1 - gate) or are treated as zero with probability 'gate'.

This models data with excess zeros compared to what a standard Negative Binomial distribution would predict.

Usage

bf.dist.zero_inflated_negative_binomial(
  mean,
  concentration,
  gate = py_none(),
  gate_logits = 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

mean	Numeric or a numeric vector. The mean of the Negative Binomial 2 distribution.
concentration	Numeric or a numeric vector. The concentration parameter of the Negative Binomial 2 distribution.
gate	numeric(1): Probability of extra zeros (between 0 and 1).
gate_logits	numeric(1): Log-odds of extra zeros.
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	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. A multi-purpose argument for shaping. 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. The number of batch dimensions to reinterpret as event dimensions (used in model building).
create_obj	Logical. If 'TRUE', returns the raw NumPyro 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 Zero-Inflated Negative Binomial distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the Zero-Inflated Negative Binomial 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.zero_inflated_negative_binomial(mean = 2, concentration = 1, gate = 0.3, sample = TRUE)

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