Package 'bliss' reference manual

Title:	Bayesian Functional Linear Regression with Sparse Step Functions
Description:	A method for the Bayesian functional linear regression model (scalar-on-function), including two estimators of the coefficient function and an estimator of its support. A representation of the posterior distribution is also available. Grollemund P-M., Abraham C., Baragatti M., Pudlo P. (2019) <doi:10.1214/18-BA1095>.
Authors:	Paul-Marie Grollemund [aut, cre], Isabelle Sanchez [ctr], Meili Baragatti [ctr]
Maintainer:	Paul-Marie Grollemund <[email protected]>
License:	GPL-3
Version:	1.1.1
Built:	2024-11-15 06:26:22 UTC
Source:	CRAN

between

Description

Check if a number belong to a given interval.

Usage

value %between% interval
value %between% interval

Arguments

`value`	a numerical value.
`interval`	a numerical vector: (lower,upper).

Value

a logical value.

Examples

1 %between% c(0,2)
2 %between% c(0,2)
3 %between% c(0,2)
1 %between% c(0,2)
2 %between% c(0,2)
3 %between% c(0,2)

BIC_model_choice

Description

Model selection with BIC criterion.

Usage

BIC_model_choice(Ks, iter, data, verbose = T)
BIC_model_choice(Ks, iter, data, verbose = T)

Arguments

`Ks`	a numerical vector containing the K values.
`iter`	an integer, the number of iteration for each run of `fit_Bliss`.
`data`	a list containing required options to run the function `fit_Bliss`.
`verbose`	write stuff if TRUE (optional).

Value

A numerical vector, the BIC values for the Bliss model for different K value.

Examples


param_sim <- list(Q=1,n=100,p=c(50),grids_lim=list(c(0,1)))
data      <- sim(param_sim,verbose=TRUE)
iter = 1e2
Ks <- 1:5

res_BIC <- BIC_model_choice(Ks,iter,data)
plot(res_BIC,xlab="K",ylab="BIC")

param_sim <- list(Q=1,n=100,p=c(50),grids_lim=list(c(0,1)))
data      <- sim(param_sim,verbose=TRUE)
iter = 1e2
Ks <- 1:5

res_BIC <- BIC_model_choice(Ks,iter,data)
plot(res_BIC,xlab="K",ylab="BIC")

bliss: Bayesian functional Linear regression with Sparse Step functions

Description

A method for the Bayesian Functional Linear Regression model (functions-on-scalar), including two estimators of the coefficient function and an estimator of its support. A representation of the posterior distribution is also available.

Author(s)

Maintainer: Paul-Marie Grollemund [email protected]

Other contributors:

Isabelle Sanchez [email protected] [contractor]
Meili Baragatti [email protected] [contractor]

Bliss_Gibbs_Sampler

Description

A Gibbs Sampler algorithm to sample the posterior distribution of the Bliss model.

Usage

Bliss_Gibbs_Sampler(data, param, verbose = FALSE)
Bliss_Gibbs_Sampler(data, param, verbose = FALSE)

Arguments

data

a list containing:

y: a numerical vector, the outcome values y_i.
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:

Q: an integer, the number of functional covariates.
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.
p: an integer, the number of time points.
basis: a character (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
phi_l: a numerical (optional). An hyperparameters related to the exponential prior on the length of the intervals. Lower values promotes wider intervals.
verbose_cpp: a boolean value (optional). Write stuff from the Rcpp scripts if TRUE.

verbose

write stuff if TRUE (optional).

Value

a list containing :

trace: a matrix, the trace of the Gibbs Sampler.
param: a list containing parameters used to run the function.

Examples


param_sim <- list(Q=1,n=25,p=50,grids_lim=list(c(0,1)),iter=2e2,K=2)
data_sim <- sim(param_sim,verbose=FALSE)
res_Bliss_Gibbs_Sampler <- Bliss_Gibbs_Sampler(data_sim,param_sim)
theta_1 <- res_Bliss_Gibbs_Sampler$trace[1,]
theta_1

param_sim <- list(Q=1,n=25,p=50,grids_lim=list(c(0,1)),iter=2e2,K=2)
data_sim <- sim(param_sim,verbose=FALSE)
res_Bliss_Gibbs_Sampler <- Bliss_Gibbs_Sampler(data_sim,param_sim)
theta_1 <- res_Bliss_Gibbs_Sampler$trace[1,]
theta_1

Bliss_Simulated_Annealing

Description

A Simulated Annealing algorithm to compute the Bliss estimate.

Usage

Bliss_Simulated_Annealing(
  beta_sample,
  posterior_sample,
  param,
  verbose_cpp = FALSE
)
Bliss_Simulated_Annealing(
  beta_sample,
  posterior_sample,
  param,
  verbose_cpp = FALSE
)

Arguments

`beta_sample`	a matrix. Each row is a coefficient function computed from the posterior sample.
`posterior_sample`	a list resulting from the `Bliss_Gibbs_Sampler` function.
`param`	a list containing: grids a list of numerical vectors, the qth vector is the grid of time points for the qth functional covariate. basis a character (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. Temp_init a nonnegative value (optional), the initial temperature for the cooling function of the Simulated Annealing algorithm. Q an integer, the number of functional covariates. p a vector of integers, the numbers of time point of each functional covariate. verbose write stuff if TRUE (optional).
`verbose_cpp`	Rcpp writes stuff if TRUE (optional).

Value

a list containing:

Bliss_estimate: a numerical vector, corresponding to the Bliss estimate of the coefficient function.
Smooth_estimate: a numerical vector, which is the posterior expectation of the coefficient function for each time points.
trace: a matrix, the trace of the algorithm.

Examples


data(data1)
data(param1)
data(res_bliss1)
param1$Q <- length(data1$x)
param1$grids <- data1$grids
param1$p <- sapply(data1$grids,length)

posterior_sample <- res_bliss1$posterior_sample
beta_sample <- compute_beta_sample(posterior_sample,param1)

res_sann <- Bliss_Simulated_Annealing(beta_sample,posterior_sample,param1)

data(data1)
data(param1)
data(res_bliss1)
param1$Q <- length(data1$x)
param1$grids <- data1$grids
param1$p <- sapply(data1$grids,length)

posterior_sample <- res_bliss1$posterior_sample
beta_sample <- compute_beta_sample(posterior_sample,param1)

res_sann <- Bliss_Simulated_Annealing(beta_sample,posterior_sample,param1)

build_Fourier_basis

Description

Define a Fourier basis to simulate functional covariate observations.

Usage

build_Fourier_basis(grid, dim, per = 2 * pi)
build_Fourier_basis(grid, dim, per = 2 * pi)

Arguments

`grid`	a numerical vector.
`dim`	a numerical value. It corresponds to `dim(basis)/2`.
`per`	a numerical value which corresponds to the period of the sine and cosine functions.

Details

See the sim_x function.

Value

a matrix. Each row is an functional observation evaluated on the grid time points.

Examples

# See the function \code{sim_x}.
# See the function \code{sim_x}.

change_grid

Description

Compute a function (evaluated on a grid) on a given (finer) grid.

Usage

change_grid(fct, grid, new_grid)
change_grid(fct, grid, new_grid)

Arguments

`fct`	a numerical vector, the function to evaluate on the new grid.
`grid`	a numerical vector, the initial grid.
`new_grid`	a numerical vector, the new grid.

Value

a numerical vector, the approximation of the function on the new grid.

Examples

grid <- seq(0,1,l=1e1)
new_grid <- seq(0,1,l=1e2)
fct <- 3*grid^2 + sin(grid*2*pi)
plot(grid,fct,type="o",lwd=2,cex=1.5)
lines(new_grid,change_grid(fct,grid,new_grid),type="o",col="red",cex=0.8)
grid <- seq(0,1,l=1e1)
new_grid <- seq(0,1,l=1e2)
fct <- 3*grid^2 + sin(grid*2*pi)
plot(grid,fct,type="o",lwd=2,cex=1.5)
lines(new_grid,change_grid(fct,grid,new_grid),type="o",col="red",cex=0.8)

choose_beta

Description

Compute a coefficient function for the Function Linear Regression model.

Usage

choose_beta(param)
choose_beta(param)

Arguments

param

a list containing:

grid: a numerical vector, the time points.
p: a numerical value, the length of the vector grid.
shape: a character vector: "smooth", "random_smooth", "simple", "simple_bis", "random_simple", "sinusoid", "flat_sinusoid" and "sharp"

Details

Several shapes are available.

Value

A numerical vector which corresponds to the coefficient function at given times points (grid).

Examples

### smooth
param <- list(p=100,grid=seq(0,1,length=100),shape="smooth")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### random_smooth
param <- list(p=100,grid=seq(0,1,length=100),shape="random_smooth")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### simple
param <- list(p=100,grid=seq(0,1,length=100),shape="simple")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="s")
### simple_bis
param <- list(p=100,grid=seq(0,1,length=100),shape="simple_bis")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="s")
### random_simple
param <- list(p=100,grid=seq(0,1,length=100),shape="random_simple")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="s")
### sinusoid
param <- list(p=100,grid=seq(0,1,length=100),shape="sinusoid")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### flat_sinusoid
param <- list(p=100,grid=seq(0,1,length=100),shape="flat_sinusoid")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### sharp
param <- list(p=100,grid=seq(0,1,length=100),shape="sharp")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### smooth
param <- list(p=100,grid=seq(0,1,length=100),shape="smooth")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### random_smooth
param <- list(p=100,grid=seq(0,1,length=100),shape="random_smooth")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### simple
param <- list(p=100,grid=seq(0,1,length=100),shape="simple")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="s")
### simple_bis
param <- list(p=100,grid=seq(0,1,length=100),shape="simple_bis")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="s")
### random_simple
param <- list(p=100,grid=seq(0,1,length=100),shape="random_simple")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="s")
### sinusoid
param <- list(p=100,grid=seq(0,1,length=100),shape="sinusoid")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### flat_sinusoid
param <- list(p=100,grid=seq(0,1,length=100),shape="flat_sinusoid")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")
### sharp
param <- list(p=100,grid=seq(0,1,length=100),shape="sharp")
beta_function <- choose_beta(param)
plot(param$grid,beta_function,type="l")

compute_beta_posterior_density

Description

Compute the posterior density of the coefficient function.

Usage

compute_beta_posterior_density(beta_sample, param)
compute_beta_posterior_density(beta_sample, param)

Arguments

beta_sample

a matrix. Each row is a coefficient function computed from the posterior sample.

param

a list containing:

grid: a numerical vector, the time points.
lims_estimate: a numerical vector, the time points.
burnin: an integer (optional), the number of iteration to drop from the Gibbs sample.
lims_kde: an integer (optional), correspond to the lims option of the kde2d funtion.
new_grid: a numerical vector (optional) to compute beta sample on a different grid.
thin: an integer (optional) to thin the posterior sample.

Details

The posterior densities correponds to approximations of the marginal posterior distribitions (of beta(t) for each t). The sample is thinned in order to reduce the correlation and the computational time of the function kde2d.

Value

An approximation of the posterior density on a two-dimensional grid (corresponds to the result of the kde2d function).

Examples


library(RColorBrewer)
data(data1)
data(param1)
data(res_bliss1)
param1$grids <- data1$grids
param1$p <- sapply(data1$grids,length)
param1$Q <- length(data1$x)

density_estimate <- compute_beta_posterior_density(res_bliss1$beta_sample,param1)

library(RColorBrewer)
data(data1)
data(param1)
data(res_bliss1)
param1$grids <- data1$grids
param1$p <- sapply(data1$grids,length)
param1$Q <- length(data1$x)

density_estimate <- compute_beta_posterior_density(res_bliss1$beta_sample,param1)

compute_beta_sample

Description

Compute the posterior coefficient function from the posterior sample.

Usage

compute_beta_sample(posterior_sample, param)
compute_beta_sample(posterior_sample, param)

Arguments

posterior_sample

a list provided by the function Bliss_Gibbs_Sampler.

param

a list containing:

K: a vector of integers, corresponding to the numbers of intervals for each covariate.
grids: a numerical vector, the observation time points.
basis: a character (optional) among : "uniform" (default), "epanechnikov", "gauss" and "triangular" which correspond to different basis functions to expand the coefficient function and the functional covariates.
Q: an integer, the number of functional covariates.
p: a vector of integers, the numbers of time points of each functional covariate.

Value

a matrix containing the coefficient function posterior sample.

Examples

data(data1)
data(param1)
data(res_bliss1)
param1$grids <- data1$grids
param1$p <- sapply(data1$grids,length)
param1$Q <- length(data1$x)
beta_sample <- compute_beta_sample(posterior_sample=res_bliss1$posterior_sample,
                                   param=param1)
data(data1)
data(param1)
data(res_bliss1)
param1$grids <- data1$grids
param1$p <- sapply(data1$grids,length)
param1$Q <- length(data1$x)
beta_sample <- compute_beta_sample(posterior_sample=res_bliss1$posterior_sample,
                                   param=param1)

compute_chains_info

Description

Compute summaries of Gibbs Sampler chains.

Usage

compute_chains_info(chain, param)
compute_chains_info(chain, param)

Arguments

chain

a list given by the Bliss_Gibbs_Sampler function.

param

a list containing:

K: a vector of integers, corresponding to the numbers of intervals for each covariate.
grids: a numerical vector, the observation time points.
basis: a vector of characters (optional) among : "uniform" (default), "epanechnikov", "gauss" and "triangular" which correspond to different basis functions to expand the coefficient function and the functional covariates.

Value

Return a list containing the estimates of mu and sigma_sq, the Smooth estimate and the chain autocorrelation for mu, sigma_sq and beta.

Examples


a=1

a=1

compute_random_walk

Description

Compute a (Gaussian) random walk.

Usage

compute_random_walk(n, p, mu, sigma, start = rep(0, n))
compute_random_walk(n, p, mu, sigma, start = rep(0, n))

Arguments

`n`	an integer, the number of random walks.
`p`	an integer, the length of the random walks.
`mu`	a numerical vector, the mean of the random walks.
`sigma`	a numerical value which is the standard deviation of the gaussian distribution used to compute the random walks.
`start`	a numerical vector (optional) which is the initial value of the random walks.

Details

See the sim_x function.

Value

a matrix where each row is a random walk.

Examples

# see the sim_x() function.
# see the sim_x() function.

compute_starting_point_sann

Description

Compute a starting point for the Simulated Annealing algorithm.

Usage

compute_starting_point_sann(beta_expe)
compute_starting_point_sann(beta_expe)

Arguments

beta_expe

a numerical vector, the expectation of the coefficient function posterior sample.

Value

a matrix with 3 columns : "m", "l" and "b". The two first columns define the begin and the end of the intervals and the third gives the mean values of each interval.

Examples

data(res_bliss1)
mystart<-compute_starting_point_sann(apply(res_bliss1$beta_sample[[1]],2,mean))
data(res_bliss1)
mystart<-compute_starting_point_sann(apply(res_bliss1$beta_sample[[1]],2,mean))

corr_matrix

Description

Compute an autocorrelation matrix.

Usage

corr_matrix(diagonal, ksi)
corr_matrix(diagonal, ksi)

Arguments

`diagonal`	a numerical vector corresponding to the diagonal.
`ksi`	a numerical value, related to the correlation.

Value

a symmetric matrix.

Examples

### Test 1 : weak autocorrelation
ksi     <- 1
diagVar <- abs(rnorm(100,50,5))
Sigma   <- corr_matrix(diagVar,ksi^2)
persp(Sigma)
### Test 2 : strong autocorrelation
ksi     <- 0.2
diagVar <- abs(rnorm(100,50,5))
Sigma   <- corr_matrix(diagVar,ksi^2)
persp(Sigma)
### Test 1 : weak autocorrelation
ksi     <- 1
diagVar <- abs(rnorm(100,50,5))
Sigma   <- corr_matrix(diagVar,ksi^2)
persp(Sigma)
### Test 2 : strong autocorrelation
ksi     <- 0.2
diagVar <- abs(rnorm(100,50,5))
Sigma   <- corr_matrix(diagVar,ksi^2)
persp(Sigma)

a list of data

Description

A data object for bliss model

Usage

data1
data1

Format

a list of data

y: y coordinate
x: x coordinate
betas: the coefficient function used to generate the data
grids: the grid of the observation times

determine_intervals

Description

Determine for which intervals a function is nonnull.

Usage

determine_intervals(beta_fct)
determine_intervals(beta_fct)

Arguments

beta_fct

a numerical vector.

Value

a matrix with 3 columns : "begin", "end" and "value". The two first columns define the begin and the end of the intervals and the third gives the mean values of each interval.

Examples

data(data1)
data(param1)
# result of res_bliss1<-fit_Bliss(data=data1,param=param1)
data(res_bliss1)
intervals <- determine_intervals(res_bliss1$Bliss_estimate[[1]])
plot(data1$grids[[1]],res_bliss1$Bliss_estimate[[1]],type="s")
for(k in 1:nrow(intervals)){
   segments(data1$grids[[1]][intervals[k,1]],intervals[k,3],
           data1$grids[[1]][intervals[k,2]],intervals[k,3],col=2,lwd=4)
}
data(data1)
data(param1)
# result of res_bliss1<-fit_Bliss(data=data1,param=param1)
data(res_bliss1)
intervals <- determine_intervals(res_bliss1$Bliss_estimate[[1]])
plot(data1$grids[[1]],res_bliss1$Bliss_estimate[[1]],type="s")
for(k in 1:nrow(intervals)){
   segments(data1$grids[[1]][intervals[k,1]],intervals[k,3],
           data1$grids[[1]][intervals[k,2]],intervals[k,3],col=2,lwd=4)
}

do_need_to_reduce

Description

Determine if it is required to reduce the size of the grid time points for each functional covariate.

Usage

do_need_to_reduce(param)
do_need_to_reduce(param)

Arguments

param

a list containing p_threshold the maximum number of time points and p the actual number of time points for each functional covariate.

Value

a boolean value.

Examples

data(param1)
param1$p <- sapply(data1$grids,length)

do_need_to_reduce(param1)
data(param1)
param1$p <- sapply(data1$grids,length)

do_need_to_reduce(param1)

dposterior

Description

Compute (non-normalized) posterior densities for a given parameter set.

Usage

dposterior(posterior_sample, data, theta = NULL)
dposterior(posterior_sample, data, theta = NULL)

Arguments

posterior_sample

a list given by the Bliss_Gibbs_Sampler function.

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.

theta

a matrix or a vector which contains the parameter set.

Details

If the theta is NULL, the posterior density is computed from the MCMC sample given in the posterior_sample.

Value

Return the (log) posterior density, the (log) likelihood and the (log) prior density for the given parameter set.

Examples

data(data1)
data(param1)
# result of res_bliss1<-fit_Bliss(data=data1,param=param1)
data(res_bliss1)
# Compute the posterior density of the MCMC sample :
res_poste <- dposterior(res_bliss1$posterior_sample,data1)
data(data1)
data(param1)
# result of res_bliss1<-fit_Bliss(data=data1,param=param1)
data(res_bliss1)
# Compute the posterior density of the MCMC sample :
res_poste <- dposterior(res_bliss1$posterior_sample,data1)

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
)
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

a list of support estimates of each functional covariate.

support_estimate_fct

another version of the support estimates.

trace_sann

a list of Q matrices which are the trace of the Simulated Annealing algorithm.

Examples

# see the vignette BlissIntro.
# see the vignette BlissIntro.

image_Bliss

Description

Plot an approximation of the posterior density.

Usage

image_Bliss(beta_posterior_density, param = list(), q = 1, to_print = TRUE)
image_Bliss(beta_posterior_density, param = list(), q = 1, to_print = TRUE)

Arguments

`beta_posterior_density`	a list. The result of the function `compute_beta_posterior_density`.
`param`	an optional list containing arguments: col_low, col_mid, col_high, ylim, xlab, ylab, title.
`q`	an integer (optional), the index of the functional covariate to plot.
`to_print`	display the plot if TRUE.

Examples


data(data1)
data(param1)
data(res_bliss1)

image_Bliss(res_bliss1$beta_posterior_density,param1,q=1)

data(data1)
data(param1)
data(res_bliss1)

image_Bliss(res_bliss1$beta_posterior_density,param1,q=1)

integrate_trapeze

Description

Trapezoidal rule to approximate an integral.

Usage

integrate_trapeze(x, y)
integrate_trapeze(x, y)

Arguments

`x`	a numerical vector, the discretization of the domain.
`y`	a numerical value, the discretization of the function to integrate.

Value

a numerical value, the approximation.

Examples

x <- seq(0,1,le=1e2)
integrate_trapeze(x,x^2)

integrate_trapeze(data1$grids[[1]],t(data1$x[[1]]))
x <- seq(0,1,le=1e2)
integrate_trapeze(x,x^2)

integrate_trapeze(data1$grids[[1]],t(data1$x[[1]]))

interpretation_plot

Description

Provide a graphical representation of the functional data with a focus on the detected periods with the Bliss method.

Usage

interpretation_plot(data, Bliss_estimate, q = 1, centered = FALSE, cols = NULL)
interpretation_plot(data, Bliss_estimate, q = 1, centered = FALSE, cols = NULL)

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.
`Bliss_estimate`	a numerical vector, the Bliss estimate.
`q`	an integer (optional), the index of the functional covariate to plot.
`centered`	a logical value (optional), If TRUE, the functional data are centered.
`cols`	a numerical vector of colours (optional).

Examples

data(data1)
data(param1)
# result of res_bliss1 <- fit_Bliss(data=data1,param=param1,verbose=TRUE)
data(res_bliss1)
interpretation_plot(data=data1,Bliss_estimate=res_bliss1$Bliss_estimate,q=1)
interpretation_plot(data=data1,Bliss_estimate=res_bliss1$Bliss_estimate,q=1,centered=TRUE)
data(data1)
data(param1)
# result of res_bliss1 <- fit_Bliss(data=data1,param=param1,verbose=TRUE)
data(res_bliss1)
interpretation_plot(data=data1,Bliss_estimate=res_bliss1$Bliss_estimate,q=1)
interpretation_plot(data=data1,Bliss_estimate=res_bliss1$Bliss_estimate,q=1,centered=TRUE)

lines_bliss

Description

Add a line to a plot obtained with image_Bliss.

Usage

lines_bliss(x, y, col = "black", lty = "solid")
lines_bliss(x, y, col = "black", lty = "solid")

Arguments

`x`	the coordinates of points in the plot.
`y`	the y coordinates of points in the plot.
`col`	a color.
`lty`	option corresponding to "linetype" of `geom_line`.

Examples


data(data1)
data(param1)
data(res_bliss1)

image_Bliss(res_bliss1$beta_posterior_density,param1,q=1) +
lines_bliss(res_bliss1$data$grids[[1]],res_bliss1$smooth_estimate[[1]])+
lines_bliss(res_bliss1$data$grids[[1]],res_bliss1$Bliss_estimate[[1]],col="purple")

data(data1)
data(param1)
data(res_bliss1)

image_Bliss(res_bliss1$beta_posterior_density,param1,q=1) +
lines_bliss(res_bliss1$data$grids[[1]],res_bliss1$smooth_estimate[[1]])+
lines_bliss(res_bliss1$data$grids[[1]],res_bliss1$Bliss_estimate[[1]],col="purple")

A list of param for bliss model

Description

A list of param for bliss model

Usage

param1
param1

Format

a list of param for bliss model

Q: the number of functional covariates
n: the sample size
p: the number of observation times
beta_shapes: the shapes of the coefficient functions
grids_lim: the range of the observation times
grids: the grids of the observation times
K: the number of intervals for the coefficient function

pdexp

Description

Probability function of a discretized Exponentiel distribution.

Usage

pdexp(a, l_values)
pdexp(a, l_values)

Arguments

`a`	a positive value, the mean of the Exponential prior.
`l_values`	a numerical value, the discrete support of the parameter l.

Value

a numerical vector, which is the prability function on l_values.

Examples

pdexp(10,seq(0,1,1))

x <- seq(0,10,le=1e3)
plot(x,dexp(x,0.5),lty=2,type="l")
lines(pdexp(0.5,1:10),type="p")
pdexp(10,seq(0,1,1))

x <- seq(0,10,le=1e3)
plot(x,dexp(x,0.5),lty=2,type="l")
lines(pdexp(0.5,1:10),type="p")

post_treatment_bliss

Description

Compute the post treatment values.

Usage

post_treatment_bliss(posterior_sample, param, data)
post_treatment_bliss(posterior_sample, param, data)

Arguments

posterior_sample

a list provided by the function Bliss_Gibbs_Sampler.

param

a list containing:

K: a vector of integers, corresponding to the numbers of intervals for each covariate.

data

a list containing required options to run the function dposterior.

Value

A list of important post treatment value: BIC, the maximum of the log likelihood and the numbre of parameters.

Examples


data(data1)
data(param1)
data(res_bliss1)

post_treatment_bliss(res_bliss1$posterior_sample,param1,data1)

data(data1)
data(param1)
data(res_bliss1)

post_treatment_bliss(res_bliss1$posterior_sample,param1,data1)

predict_bliss

Description

Compute predictions.

Usage

predict_bliss(x, grids, burnin, posterior_sample, Smooth_estimate)
predict_bliss(x, grids, burnin, posterior_sample, Smooth_estimate)

Arguments

`x`	a list containing the design matrices related to the functional covariates. Must be similar to the result of the function `sim_x`.
`grids`	a list of numerical vectors, the qth vector is the grid of time points for the qth functional covariate.
`burnin`	an integer (optional), the number of iteration to drop from the posterior sample.
`posterior_sample`	a list provided by the function `Bliss_Gibbs_Sampler`.
`Smooth_estimate`	one of the objects resulting from `Bliss_Simulated_Annealing`.

Value

A vector of predictions for each individual data x.

Examples


data(data1)
data(param1)
data(res_bliss1)

predict_bliss(data1$x,data1$grids,50,res_bliss1$posterior_sample,res_bliss1$smooth_estimate)

data(data1)
data(param1)
data(res_bliss1)

predict_bliss(data1$x,data1$grids,50,res_bliss1$posterior_sample,res_bliss1$smooth_estimate)

predict_bliss_distribution

Description

Compute the distribution of the predictions.

Usage

predict_bliss_distribution(x, grids, burnin, posterior_sample, beta_sample)
predict_bliss_distribution(x, grids, burnin, posterior_sample, beta_sample)

Arguments

`x`	a list containing the design matrices related to the functional covariates. Must be similar to the result of the function `sim_x`.
`grids`	a list of numerical vectors, the qth vector is the grid of time points for the qth functional covariate.
`burnin`	an integer (optional), the number of iteration to drop from the posterior sample.
`posterior_sample`	a list provided by the function `Bliss_Gibbs_Sampler`.
`beta_sample`	a list provided by the function `compute_beta_sample`.

Value

A matrix containing predictions for each individual data x.

Examples


data(data1)
data(param1)
data(res_bliss1)

predict_bliss_distribution(data1$x,data1$grids,50,res_bliss1$posterior_sample,
   res_bliss1$beta_sample)

data(data1)
data(param1)
data(res_bliss1)

predict_bliss_distribution(data1$x,data1$grids,50,res_bliss1$posterior_sample,
   res_bliss1$beta_sample)

Print a bliss Object

Description

Print a bliss Object

Usage

printbliss(x, ...)
printbliss(x, ...)

Arguments

`x`	input bliss Object
`...`	further arguments passed to or from other methods

Examples

# See fit_Bliss() function
# See fit_Bliss() function

reduce_x

Description

Reduce the number of time points.

Usage

reduce_x(data, param)
reduce_x(data, param)

Arguments

`data`	similar to `fit_Bliss`.
`param`	a list containing values `Q`, `p` and `p`

Value

a numerical value, the approximation.

Examples

param <- list(Q=1,n=10,p=c(150),grids_lim=list(c(0,1)))
data <- sim(param)

data(param1)
param1$n <- nrow(data$x[[1]])
param1$p <- sapply(data$grids,length)
param1$Q <- length(data$x)

data <- reduce_x(data,param1)
param <- list(Q=1,n=10,p=c(150),grids_lim=list(c(0,1)))
data <- sim(param)

data(param1)
param1$n <- nrow(data$x[[1]])
param1$p <- sapply(data$grids,length)
param1$Q <- length(data$x)

data <- reduce_x(data,param1)

A result of the BliSS method

Description

A result of the BliSS method

Usage

res_bliss1
res_bliss1

Format

a Bliss object (list)

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

see the description of the object data1.

posterior_sample

a list containing (for each chain) the result of the Bliss_Gibbs_Sampler function.

Smooth_estimate

a list containing the Smooth estimates of the coefficient functions.

support_estimate

a list containing the estimations of the support.

support_estimate_fct

a list containing the estimation of the support.

trace_sann

a list containing (for each chain) the trace of the Simulated Annealing algorithm.

sigmoid

Description

Compute a sigmoid function.

Usage

sigmoid(x, asym = 1, v = 1)
sigmoid(x, asym = 1, v = 1)

Arguments

`x`	a numerical vector, time points.
`asym`	a numerical value (optional), the asymptote of the sigmoid function.
`v`	a numerical value (optional), related to the slope at the origin.

Details

see the function sim_x.

Value

a numerical vector.

Examples

## Test 1 :
x <- seq(-7,7,0.1)
y <- sigmoid(x)
plot(x,y,type="l",main="Sigmoid function")
## Test 2 :
x  <- seq(-7,7,0.1)
y  <- sigmoid(x)
y2 <- sigmoid(x,asym=0.5)
y3 <- sigmoid(x,v   =  5)
plot(x,y,type="l",main="Other sigmoid functions")
lines(x,y2,col=2)
lines(x,y3,col=3)
## Test 1 :
x <- seq(-7,7,0.1)
y <- sigmoid(x)
plot(x,y,type="l",main="Sigmoid function")
## Test 2 :
x  <- seq(-7,7,0.1)
y  <- sigmoid(x)
y2 <- sigmoid(x,asym=0.5)
y3 <- sigmoid(x,v   =  5)
plot(x,y,type="l",main="Other sigmoid functions")
lines(x,y2,col=2)
lines(x,y3,col=3)

sigmoid_sharp

Description

Compute a sharp sigmoid function.

Usage

sigmoid_sharp(x, loc = 0, ...)
sigmoid_sharp(x, loc = 0, ...)

Arguments

`x`	a numerical vector, time points.
`loc`	a numerical value (optional), the time of the sharp.
`...`	Arguments (optional) for the function sigmoid.

Details

see the function sim_x.

Value

a numerical vector.

Examples

## Test 1 :
x <- seq(-7,7,0.1)
y <- sigmoid_sharp(x)
plot(x,y,type="l",main="Sharp sigmoid")
## Test 2 :
x  <- seq(-7,7,0.1)
y  <- sigmoid_sharp(x,loc=3)
y2 <- sigmoid_sharp(x,loc=3,asym=0.5)
y3 <- sigmoid_sharp(x,loc=3,v   =  5)
plot(x,y,type="l",main="Other sharp sigmoids")
lines(x,y2,col=2)
lines(x,y3,col=3)
## Test 1 :
x <- seq(-7,7,0.1)
y <- sigmoid_sharp(x)
plot(x,y,type="l",main="Sharp sigmoid")
## Test 2 :
x  <- seq(-7,7,0.1)
y  <- sigmoid_sharp(x,loc=3)
y2 <- sigmoid_sharp(x,loc=3,asym=0.5)
y3 <- sigmoid_sharp(x,loc=3,v   =  5)
plot(x,y,type="l",main="Other sharp sigmoids")
lines(x,y2,col=2)
lines(x,y3,col=3)

sim

Description

Simulate a dataset for the Function Linear Regression model.

Usage

sim(param, verbose = FALSE)
sim(param, verbose = FALSE)

Arguments

param

a list containing:

beta_shapes: a character vector. The qth item indicates the shape of the coefficient function associated to the qth functional covariate.
beta_functions: a list containing numerical vectors to define the beta functions
n: an integer, the sample size.
p: a vector of integers, the qth component is the number of times for the qth covariate.
Q: an integer, the number of functional covariates.
autocorr_diag: a list of numerical vectors (optional), the qth vector is the diagonal of the autocorrelation matrix of the qth functional covariate.
autocorr_spread: a vector of numerical values (optional) which are related to the autocorrelation of the functional covariates.
grids: a list of numerical vectors (optional), the qth vector is the grid of time points for the qth functional covariate.
grids_lim: a list of numerical vectors (optional), the qth item is the lower and upper boundaries of the domain for the qth functional covariate.
link: a function (optional) to simulate data from the Generalized Functional Linear Regression model.
mu: a numerical value (optional), the 'true' intercept of the model.
r: a nonnegative value (optional), the signal to noise ratio.
x_shapes: a character vector (optional). The qth item indicates the shape of the functional covariate observations.

verbose

write stuff if TRUE.

Value

a list containing:

Q: an integer, the number of functional covariates.
y: a numerical vector, the outcome observations.
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.
betas: a list of numerical vectors, the qth vector is the 'true' coefficient function associated to the qth covariate on a grid of time points given with grids.

Examples

library(RColorBrewer)
param <- list(Q=2,n=25,p=c(50,50),grids_lim=list(c(0,1),c(-1,2)))
data <- sim(param)
data$y
cols <- colorRampPalette(brewer.pal(9,"YlOrRd"))(10)
q=2
matplot(data$grids[[q]],t(data$x[[q]]),type="l",lty=1,col=cols)
plot(data$grids[[q]],data$betas[[q]],type="l")
abline(h=0,lty=2,col="gray")
library(RColorBrewer)
param <- list(Q=2,n=25,p=c(50,50),grids_lim=list(c(0,1),c(-1,2)))
data <- sim(param)
data$y
cols <- colorRampPalette(brewer.pal(9,"YlOrRd"))(10)
q=2
matplot(data$grids[[q]],t(data$x[[q]]),type="l",lty=1,col=cols)
plot(data$grids[[q]],data$betas[[q]],type="l")
abline(h=0,lty=2,col="gray")

sim_x

Description

Simulate functional covariate observations.

Usage

sim_x(param)
sim_x(param)

Arguments

param

a list containing :

grid: a numerical vector, the observation times.
n: an integer, the sample size.
p: an integer, the number of observation times.
diagVar: a numerical vector (optional), the diagonal of the autocorrelation matrix.
dim: a numerical value (optional), the dimension of the Fourier basis, if "shape" is "Fourier" or "Fourier2".
ksi: a numerical value (optional) related to the observations correlation.
x_shape: a character vector (optional), the shape of the observations.

Details

Several shape are available for the observations: "Fourier", "Fourier2", "random_walk", "random_sharp", "uniform", "gaussian", "mvgauss", "mvgauss_different_scale", "mvgauss_different_scale2", "mvgauss_different_scale3" and "mvgauss_different_scale4".

Value

a matrix which contains the functional covariate observations at time points given by grid.

Examples

library(RColorBrewer)
### uniform
param <- list(n=15,p=100,grid=seq(0,1,length=100),x_type="uniform")
x <- sim_x(param)
cols <- colorRampPalette(brewer.pal(9,"YlOrRd"))(15)
matplot(param$grid,t(x),type="l",lty=1,col=cols)
library(RColorBrewer)
### uniform
param <- list(n=15,p=100,grid=seq(0,1,length=100),x_type="uniform")
x <- sim_x(param)
cols <- colorRampPalette(brewer.pal(9,"YlOrRd"))(15)
matplot(param$grid,t(x),type="l",lty=1,col=cols)

support_estimation

Description

Compute the support estimate.

Usage

support_estimation(beta_sample, param)
support_estimation(beta_sample, param)

Arguments

`beta_sample`	the result of the function `compute_beta_sample`.
`param`	a list containing the value `Q` and an optional parameter `gamma`.

Value

a list containing:

alpha: a numerical vector. The approximated posterior probabilities that the coefficient function support covers t for each time points t.
estimate: a numerical vector, the support estimate.
estimate_fct: a numerical vector, another version of the support estimate.

Examples

data(data1)
data(param1)
data(res_bliss1)
param1$Q <- length(data1$x)

res_support <- support_estimation(res_bliss1$beta_sample,param1)
data(data1)
data(param1)
data(res_bliss1)
param1$Q <- length(data1$x)

res_support <- support_estimation(res_bliss1$beta_sample,param1)

Package 'bliss'

Help Index

between

Description

Usage

Arguments

Value

Examples

BIC_model_choice

Description

Usage

Arguments

Value

Examples

bliss: Bayesian functional Linear regression with Sparse Step functions

Description

Author(s)

See Also

Bliss_Gibbs_Sampler

Description

Usage

Arguments

Value

Examples

Bliss_Simulated_Annealing

Description

Usage

Arguments

Value

Examples

build_Fourier_basis

Description

Usage

Arguments

Details

Value

Examples

change_grid

Description

Usage

Arguments

Value

Examples

choose_beta

Description

Usage

Arguments

Details

Value

Examples

compute_beta_posterior_density

Description

Usage

Arguments

Details

Value

Examples

compute_beta_sample

Description

Usage

Arguments

Value

Examples

compute_chains_info

Description

Usage

Arguments

Value

Examples

compute_random_walk

Description

Usage

Arguments

Details

Value

Examples

compute_starting_point_sann

Description

Usage

Arguments