rho_j_BRR: rho_j Importance Sampling Step
In rchan26/hierarchicalFusion: Divide-and-Conquer Monte Carlo Fusion

rho_j_BRR

R Documentation

rho_j Importance Sampling Step

Description

rho_j Importance Sampling weighting for Bayesian robust regression

Usage

rho_j_BRR(
  particle_set,
  m,
  time_mesh,
  dim,
  data_split,
  nu,
  sigma,
  prior_means,
  prior_variances,
  C,
  precondition_matrices,
  inv_precondition_matrices,
  Lambda,
  resampling_method = "multi",
  ESS_threshold = 0.5,
  sub_posterior_means = NULL,
  adaptive_mesh = FALSE,
  adaptive_mesh_parameters = NULL,
  record = FALSE,
  diffusion_estimator,
  beta_NB = 10,
  gamma_NB_n_points = 2,
  seed = NULL,
  n_cores = parallel::detectCores(),
  cl = NULL,
  level = 1,
  node = 1,
  print_progress_iters = 1000
)

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 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`	overall number of sub-posteriors
`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))
`sub_posterior_means`	matrix with m rows and d 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
`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
`cl`	an object of class "cluster" for parallel computation in R. If none is passed, then one is created and used within this function
`level`	indicates which level this is for the hierarchy (default 1)
`node`	indicates which node this is for the hierarchy (default 1)
`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

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

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

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
k4_choice: which of the roots of k4 were chosen