ea_multiGaussian_DL_PT: Diffusion probability for the Exact Algorithm for Langevin...

In rchan26/hierarchicalFusion: Divide-and-Conquer Monte Carlo Fusion

Diffusion probability for the Exact Algorithm for Langevin diffusion for multivariate tempered Gaussian distribution

Description

Simulate Langevin diffusion using the Exact Algorithm where pi = multivariate tempered Gaussian distribution

Usage

ea_multiGaussian_DL_PT(
  x0,
  y,
  s,
  t,
  dim,
  mu,
  inv_Sigma,
  inv_Sigma_Z = transform_mats$to_X %*% inv_Sigma %*% transform_mats$to_X,
  beta,
  precondition_mat,
  transform_mats,
  diffusion_estimator = "Poisson",
  beta_NB = 10,
  gamma_NB_n_points = 2,
  logarithm
)

Arguments

x0	start value (vector of length dim)
y	end value (vector of length dim)
s	start time
t	end time
dim	dimension
mu	vector of length dim for mean
inv_Sigma	dim x dim inverse covariance matrix
beta	real value
precondition_mat	precondition matrix (if non-identity matrix, it should be the estimated covariance matrix, i.e. a matrix close to solve(inv_Sigma) - could run into problems if this is not the case since a trick is used to compute the bounds to avoid evaluating phi at 3^d points)
transform_mats	list of transformation matrices where transform_mats$to_Z is the transformation matrix to Z space and transform_mats$to_X is the transformation matrix to X space
diffusion_estimator	choice of unbiased estimator for the Exact Algorithm between "Poisson" (default) for Poisson estimator and "NB" for Negative Binomial estimator
beta_NB	beta parameter for Negative Binomial estimator (default 10)
gamma_NB_n_points	number of points used in the trapezoidal estimation of the integral found in the mean of the negative binomial estimator (default is 2)
logarithm	logical value to determine if log probability is returned (TRUE) or not (FALSE)

Value

acceptance probability of simulating Langevin diffusion with pi = multivariate tempered Gaussian distribution

rchan26/hierarchicalFusion documentation built on Sept. 11, 2022, 10:30 p.m.