bal_binary_GBF_multiGaussian: (Balanced Binary) D&C Generalised Bayesian Fusion using SMC

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

(Balanced Binary) D&C Generalised Bayesian Fusion using SMC

Description

(Balanced Binary) D&C Generalised Bayesian Fusion with multivariate Gaussian target

Usage

bal_binary_GBF_multiGaussian(
  N_schedule,
  m_schedule,
  time_mesh = NULL,
  base_samples,
  L,
  dim,
  mean_vecs,
  Sigmas,
  C,
  precondition = TRUE,
  resampling_method = "multi",
  ESS_threshold = 0.5,
  adaptive_mesh = FALSE,
  mesh_parameters = NULL,
  diffusion_estimator = "Poisson",
  beta_NB = 10,
  gamma_NB_n_points = 2,
  seed = NULL,
  n_cores = parallel::detectCores()
)

Arguments

N_schedule	vector of length (L-1), where N_schedule[l] is the number of samples per node at level l
m_schedule	vector of length (L-1), where m_schedule[l] is the number of samples to fuse for level l
time_mesh	time mesh used in Bayesian Fusion. This can either be a vector which will be used for each node in the tree, or it can be passed in as NULL, where a recommended mesh will be generated using the parameters passed into mesh_parameters
base_samples	list of length C, where base_samples[[c]] contains the samples for the c-th node in the level
L	total number of levels in the hierarchy
dim	dimension
precondition	either a logical value to determine if preconditioning matrices are used (TRUE - and is set to be the variance of the sub-posterior samples) or not (FALSE - and is set to be the identity matrix for all sub-posteriors), or a list of length C where precondition[[c]] is the preconditioning matrix for sub-posterior c. Default is TRUE
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)
adaptive_mesh	logical value to indicate if an adaptive mesh is used (default is FALSE)
mesh_parameters	list of parameters used for 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
mu	vector of length dim for mean
Sigma	dim x dim covariance matrix

Value

A list with components:

particles

list of length (L-1), where particles[[l]][[i]] are the particles for level l, node i

proposed_samples

list of length (L-1), where proposed_samples[[l]][[i]] are the proposed samples for level l, node i

time

list of length (L-1), where time[[l]][[i]] is the run time for level l, node i

time_mesh_used

list of length (L-1), where time_mesh_used[[l]][[i]] is the time_mesh that was used for level l, node i

ESS

list of length (L-1), where ESS[[l]][[i]] is the effective sample size of the particles after each step BEFORE deciding whether or not to resample for level l, node i

CESS

list of length (L-1), where CESS[[l]][[i]] is the conditional effective sample size of the particles after each step

resampled

list of length (L-1), where resampled[[l]][[i]] is a boolean value to record if the particles were resampled after each step; rho and Q for level l, node i

E_nu_j

list of length (L-1), where E_nu_j[[l]][[i]] is the approximation of the average variation of the trajectories at each time step for level l, node i

chosen

list of length (L-1), where chosen[[l]][[i]] indicates which term was chosen if using an adaptive mesh at each time step for level l, node i

mesh_terms

list of length (L-1), where mesh_terms[[l]][[i]] indicates the evaluated terms in deciding the mesh at each time step for level l, node i

k4_choice

list of length (L-1), where k4_choice[[l]][[i]]] indicates which of the roots of k4 were chosen at each time step for level l, node i

precondition_matrices

preconditioning matrices used in the algorithm for each node

diffusion_times

vector of length (L-1), where diffusion_times[l] are the times for fusion in level l

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