fit_Bliss: fit_Bliss
In bliss: Bayesian Functional Linear Regression with Sparse Step Functions

fit_Bliss

R Documentation

fit_Bliss

Description

Fit the Bayesian Functional Linear Regression model (with Q functional covariates).

Usage

fit_Bliss(
  data,
  param,
  sann = TRUE,
  compute_density = TRUE,
  support_estimate = TRUE,
  sann_trace = FALSE,
  verbose = TRUE
)

Arguments

`data`	a list containing: y a numerical vector, the outcomes. x a list of matrices, the qth matrix contains the observations of the qth functional covariate at time points given by `grids`. grids a list of numerical vectors, the qth vector is the grid of time points for the qth functional covariate.
`param`	a list containing: iter an integer, the number of iterations of the Gibbs sampler algorithm. K a vector of integers, corresponding to the numbers of intervals for each covariate. basis a character vector (optional). The possible values are "uniform" (default), "epanechnikov", "gauss" and "triangular" which correspond to different basis functions to expand the coefficient function and the functional covariates burnin an integer (optional), the number of iteration to drop from the posterior sample. iter_sann an integer (optional), the number of iteration of the Simulated Annealing algorithm. k_max an integer (optional), the maximal number of intervals for the Simulated Annealing algorithm. l_max an integer (optional), the maximal interval length for the Simulated Annealing algorithm. lims_kde an integer (optional), correspond to the `lims` option of the `kde2d` funtion. new_grids a list of Q vectors (optional) to compute beta samples on different grids. Temp_init a nonnegative value (optional), the initial temperature for the cooling function of the Simulated Annealing algorithm. thin an integer (optional) to thin the posterior sample. times_sann an integer (optional), the number of times the algorithm will be executed times_sann an integer (optional), the number of times the algorithm will be executed allow_reducing a boolean value (optional), indicate if the function is allowed to reduce the number of sample times of each functional covariate. verbose_cpp a boolean value (optional). Write stuff from the Rcpp scripts if TRUE.
`sann`	a logical value. If TRUE, the Bliss estimate is computed with a Simulated Annealing Algorithm. (optional)
`compute_density`	a logical value. If TRUE, the posterior density of the coefficient function is computed. (optional)
`support_estimate`	a logical value. If TRUE, the estimate of the coefficient function support is computed. (optional)
`sann_trace`	a logical value. If TRUE, the trace of the Simulated Annealing algorithm is included into the result object. (optional)
`verbose`	write stuff if TRUE (optional).

Value

return a list containing:

alpha

a list of Q numerical vector. Each vector is the function alpha(t) associated to a functional covariate. For each t, alpha(t) is the posterior probabilities of the event "the support covers t".

beta_posterior_density

a list of Q items. Each item contains a list containing information to plot the posterior density of the coefficient function with the image function.

grid_t: a numerical vector: the x-axis.
grid_beta_t: a numerical vector: the y-axis.
density: a matrix: the z values.
new_beta_sample: a matrix: beta sample used to compute the posterior densities.

beta_sample

a list of Q matrices. The qth matrix is a posterior sample of the qth functional covariates.

Bliss_estimate

a list of numerical vectors corresponding to the Bliss estimates of each functional covariates.

data

a list containing the data.

posterior_sample

a list of information about the posterior sample: the trace matrix of the Gibbs sampler, a list of Gibbs sampler parameters and the posterior densities.

support_estimate