R/multi_variate_student_t.R

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

#' @title 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 \deqn{ x \in R^d } is given by:

#' \deqn{
#' 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:
#' * \deqn{ \Gamma(\cdot) } is the Gamma function.
#' * \deqn{ \mu } is the mean vector.
#' * \deqn{ \Sigma } is the scale (covariance) matrix.
#' * \deqn{ \nu } is the degrees of freedom.
#' * \deqn{ d } is the dimensionality of \deqn{ \mathbf{x}}.
#'
#' @param df A numeric vector representing degrees of freedom, must be positive.
#' @param loc A numeric vector representing the location vector (mean) of the distribution.
#' @param scale_tril A numeric matrix defining the scale (lower triangular matrix).
#' @param 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.
#' @param event An integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
#' @param mask A logical vector. Optional boolean array to mask observations.
#' @param create_obj A logical value. If `TRUE`, returns the raw BI distribution object instead of creating a sample site.
#' @param validate_args Logical: Whether to validate parameter values.  Defaults to `reticulate::py_none()`.
#' @param 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`.
#' @param 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.
#' @param 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`.
#' @param 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'.
#' @param to_jax Boolean. Indicates whether to return a JAX array or not.
#'
#' @return
#'  - When \code{sample=FALSE}, a BI Multivariate Student's t distribution object (for model building).
#'
#'  - When \code{sample=TRUE}, a JAX array of samples drawn from the Multivariate Student's t distribution (for direct sampling).
#'
#'  - When \code{create_obj=TRUE}, the raw BI distribution object (for advanced use cases).
#'
#' @seealso \url{https://num.pyro.ai/en/stable/distributions.html#multivariatestudentt}
#'
#' @examples
#' \donttest{
#' 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)
#' }
#' @export
bf.dist.multivariate_student_t=function(df, loc=0.0, 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) {
     shape=do.call(tuple, as.list(as.integer(shape)))
     reticulate::py_run_string("def is_none(x): return x is None")
     if (!.BF_env$.py$is_none(seed)){seed=as.integer(seed);}
     .BF_env$.bf_instance$dist$multivariate_student_t(
       df = .BF_env$jnp$array(df),
       loc = .BF_env$jnp$array(loc),
       scale_tril = .BF_env$jnp$array(scale_tril),
       validate_args= validate_args,  name= name,  obs= obs,  mask= mask,  sample= sample,  seed= seed,  shape= shape,  event= event,  create_obj= create_obj,   to_jax = to_jax)
}