bf.dist.car: Conditional Autoregressive (CAR) Distribution

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

Conditional Autoregressive (CAR) Distribution

Description

The CAR distribution models a vector of variables where each variable is a linear combination of its neighbors in a graph. The CAR model captures spatial dependence in areal data by modeling each observation as conditionally dependent on its neighbors. It specifies a joint distribution of a vector of random variables

\mathbf{y} = (y_1, y_2, \dots, y_N)

based on their conditional distributions, where each

y_i

is conditionally independent of all other variables given its neighbors. - Application: Widely used in disease mapping, environmental modeling, and spatial econometrics to account for spatial autocorrelation.

Usage

bf.dist.car(
  loc,
  correlation,
  conditional_precision,
  adj_matrix,
  is_sparse = FALSE,
  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

loc	Numeric vector, matrix, or array representing the mean of the distribution.
correlation	Numeric vector, matrix, or array representing the correlation between variables.
conditional_precision	Numeric vector, matrix, or array representing the precision of the distribution.
adj_matrix	Numeric vector, matrix, or array representing the adjacency matrix defining the graph.
is_sparse	Logical indicating whether the adjacency matrix is sparse. Defaults to 'FALSE'.
validate_args	Logical indicating whether to validate arguments. 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. 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. 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 CAR distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the CAR 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.car(
  loc = c(1.,2.),
  correlation = 0.9,
  conditional_precision = 1.,
  adj_matrix = matrix(c(1,0,0,1), nrow = 2),
  sample = TRUE
 )

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