rho_j_multiGaussian: rho_j Importance Sampling Step

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

rho_j Importance Sampling Step

Description

rho_j Importance Sampling weighting for bivariate Gaussian distributions

Usage

rho_j_multiGaussian(
  particle_set,
  m,
  time_mesh,
  dim,
  mean_vecs,
  inv_Sigmas,
  precondition_matrices,
  inv_precondition_matrices,
  Lambda,
  resampling_method = "multi",
  ESS_threshold = 0.5,
  sub_posterior_means = NULL,
  adaptive_mesh = FALSE,
  adaptive_mesh_parameters = NULL,
  diffusion_estimator = "Poisson",
  beta_NB = 10,
  gamma_NB_n_points = 2,
  seed = NULL,
  n_cores = parallel::detectCores()
)

Arguments

particle_set	particles set prior to Q importance sampling step
m	number of sub-posteriors to combine
time_mesh	time mesh used in Bayesian Fusion
dim	dimension
mean_vecs	list of length m, where mean_vecs[[c]] is a vector of length dim for the mean of sub-posterior c
inv_Sigmas	list of length m, where inv_Sigmas[[c]] is a dim x dim inverse covariance matrix for sub-posterior c
precondition_matrices	list of length m, where precondition_matrices[[c]] is the precondition matrix for sub-posterior c
inv_precondition_matrices	list of length m, where inv_precondition_matrices[[c]] is the inverse precondition matrix for sub-posterior c
Lambda	inverse of the sum of the inverse precondition matrices (which can be computed using inverse_sum_matrices(inv_precondition_matrices))
resampling_method	method to be used in resampling, default is multinomial resampling ('multi'). Other choices are stratified resampling ('strat'), systematic resampling ('system'), residual resampling ('resid')
ESS_threshold	number between 0 and 1 defining the proportion of the number of samples that ESS needs to be lower than for resampling (i.e. resampling is carried out only when ESS < N*ESS_threshold)
sub_posterior_means	matrix with m rows and dim columns, where sub_posterior_means[c,] is the sub-posterior mean of sub-posterior c
adaptive_mesh	logical value to indicate if an adaptive mesh is used (default is FALSE)
adaptive_mesh_parameters	list of parameters used for adaptive mesh
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)
seed	seed number - default is NULL, meaning there is no seed
n_cores	number of cores to use

Value

A list with components:

particle_set

updated particle set after the iterative rho_j steps

proposed_samples

proposal samples for the last time step

time

elapsed time of each step of the algorithm

ESS

effective sample size of the particles after each step

CESS

conditional effective sample size of the particles after each step

resampled

boolean value to indicate if particles were resampled after each time step

E_nu_j

approximation of the average variation of the trajectories at each time step

chosen

which term was chosen if using an adaptive mesh at each time step

mesh_terms

the evaluated terms in deciding the mesh at each time step

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