bal_binary_GBF_BRR: (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 using SMC for Bayesian Logistic Regression

Usage

bal_binary_GBF_BRR(
  N_schedule,
  m_schedule,
  time_mesh = NULL,
  base_samples,
  L,
  dim,
  data_split,
  nu,
  sigma,
  prior_means,
  prior_variances,
  C,
  precondition = TRUE,
  resampling_method = "multi",
  ESS_threshold = 0.5,
  adaptive_mesh = FALSE,
  mesh_parameters = NULL,
  record = FALSE,
  diffusion_estimator = "Poisson",
  beta_NB = 10,
  gamma_NB_n_points = 2,
  seed = NULL,
  n_cores = parallel::detectCores(),
  print_progress_iters = 1000
)

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[k] is the number of samples to fuse for level k
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 of the predictors (= p+1)
data_split	list of length m where each item is a list of length 4 where for c=1,...,m, data_split[[c]]$y is the vector for y responses and data_split[[c]]$X is the design matrix for the covariates for sub-posterior c
nu	degrees of freedom in t-distribution
sigma	scale parameter in t-distribution
prior_means	prior for means of predictors
prior_variances	prior for variances of predictors
C	number of sub-posteriors at the base level
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 (1/start_beta) 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 ('strat'), systematic ('system'), residual ('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)
record	logical value indicating if variables such as E[nu_j], chosen, mesh_terms and k4_choice should be recorded at each iteration and returned (see return variables for this function) - default is FALSE
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
print_progress_iters	number of iterations between each progress update (default is 1000). If NULL, progress will only be updated when importance sampling is finished
adaptive_mesh_parameters	list of parameters used for adaptive mesh

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

elapsed_time

list of length (L-1), where elapsed_time[[l]][[i]] is the elapsed time of each step of the algorithm for level l, node i

time_mesh

list of length (L-1), where time_mesh[[l]][[i]] is the time_mesh 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 ESS[[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

precondition_matrices

pre-conditioning matrices that were used

sub_posterior_means

sub-posterior means that were used

recommended_mesh

list of length (L-1), where recommended_mesh[[l]][[i]] is the recommended mesh for level l, node i

data_inputs

list of length (L-1), where data_inputs[[l]][[i]] is the data input for the sub-posterior in level l, node i

If record is set to TRUE, additional components will be returned:

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

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