bf.dist.euler_maruyama: Euler-Maruyama method

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

Euler-Maruyama method

Description

Euler-Maruyama methode is a method for the approximate numerical solution of a stochastic differential equation (SDE). It simulates the solution to an SDE by iteratively applying the Euler method to each time step, incorporating a random perturbation to account for the diffusion term.

Usage

bf.dist.euler_maruyama(
  t,
  sde_fn,
  init_dist,
  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

t	A numeric vector representing the discretized time steps.
sde_fn	A function that takes the current state and time as input and returns the drift and diffusion coefficients.
init_dist	The initial distribution of the system.
validate_args	A logical value indicating whether to validate the arguments. Defaults to 'TRUE'.
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. 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 specifying the shape of the output tensor. Defaults to 'NULL'.
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 Euler-Maruyama distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the Euler-Maruyama distribution (for direct sampling).

- When create_obj=TRUE, the raw BI distribution object (for advanced use cases).

Examples

library(BayesForge)
m=importBF(platform='cpu')
ornstein_uhlenbeck_sde <- function(x, t) {
 # This function models dX = -theta * X dt + sigma dW
 theta <- 1.0
 sigma <- 0.5

 drift <- -theta * x
 diffusion <- sigma

 # Return a list of two elements: drift and diffusion
 # reticulate will convert this to a Python tuple
 return(list(drift, diffusion))
}
bf.dist.euler_maruyama(
t=c(0.0, 0.1, 0.2),
sde_fn = ornstein_uhlenbeck_sde,
init_dist=bf.dist.normal(0.0, 1.0, create_obj=TRUE),
sample = TRUE)

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