Type:	Package
Title:	Bayesian Lasso Regression and Tools for the Lasso Distribution
Version:	0.3.5
Date:	2025-07-21
Maintainer:	Mohammad Javad Davoudabadi <mohammad.davoudabadi@sydney.edu.au>
Description:	Implements Bayesian Lasso regression using efficient Gibbs sampling algorithms, including modified versions of the Hans and Park–Casella (PC) samplers. Includes functions for working with the Lasso distribution, such as its density, cumulative distribution, quantile, and random generation functions, along with moment calculations. Also includes a function to compute the Mills ratio. Designed for sparse linear models and suitable for high-dimensional regression problems.
License:	GPL-3
Imports:	Rcpp (≥ 1.0.12)
LinkingTo:	Rcpp, RcppNumerical, RcppArmadillo, RcppEigen, RcppClock
RoxygenNote:	7.3.2
Encoding:	UTF-8
URL:	https://garthtarr.github.io/BayesianLasso/, https://github.com/garthtarr/BayesianLasso
VignetteBuilder:	knitr
Suggests:	knitr, rmarkdown, monomvn, bayeslm, rstan, bayesreg, lars, Ecdat, testthat (≥ 3.0.0), MASS
Config/testthat/edition:	3
BugReports:	https://github.com/garthtarr/BayesianLasso/issues
NeedsCompilation:	yes
Packaged:	2025-07-25 04:25:11 UTC; mjava
Author:	John Ormerod [aut, cph], Mohammad Javad Davoudabadi [aut, cre, cph], Garth Tarr [aut, cph], Samuel Mueller [aut, cph], Jonathon Tidswell [aut, cph]
Repository:	CRAN
Date/Publication:	2025-07-28 18:30:07 UTC

The Lasso Distribution

Description

Provides functions related to the Lasso distribution, including the normalizing constant, probability density function, cumulative distribution function, quantile function, and random number generation for given parameters a, b, and c. Additional utilities include the Mills ratio, expected value, and variance of the distribution. The package also implements modified versions of the Hans and Park–Casella Gibbs sampling algorithms for Bayesian Lasso regression.

Usage

zlasso(a, b, c, logarithm)
dlasso(x, a, b, c, logarithm)
plasso(q, a, b, c)
qlasso(p, a, b, c)
rlasso(n, a, b, c)
elasso(a, b, c)
vlasso(a, b, c)
mlasso(a, b, c)
MillsRatio(d)
Modified_Hans_Gibbs(X, y, a1, b1, u1, v1,
              nsamples, beta_init, lambda_init, sigma2_init, verbose)
Modified_PC_Gibbs(X, y, a1, b1, u1, v1, 
              nsamples, lambda_init, sigma2_init, verbose)

Arguments

Details

If X \sim \text{Lasso}(a, b, c) then its density function is:

p(x;a,b,c) = Z^{-1} \exp\left(-\frac{1}{2} a x^2 + bx - c|x| \right)

where x \in \mathbb{R}, a > 0, b \in \mathbb{R}, c > 0, and Z is the normalizing constant.

More details are included for the CDF, quantile function, and normalizing constant in the original documentation.

Value

• zlasso, dlasso, plasso, qlasso, rlasso, elasso, vlasso, mlasso, MillsRatio: return the corresponding scalar or vector values related to the Lasso distribution and a numeric value representing the Mills ratio.

• Modified_Hans_Gibbs: returns a list containing:

  mBeta

  Matrix of MCMC samples for the regression coefficients \beta, with nsamples rows and p columns.

  vsigma2

  Vector of MCMC samples for the error variance \sigma^2.

  vlambda2

  Vector of MCMC samples for the shrinkage parameter \lambda^2.

  mA

  Matrix of sampled values for parameter a_j of the Lasso distribution for each \beta_j.

  mB

  Matrix of sampled values for parameter b_j of the Lasso distribution for each \beta_j.

  mC

  Matrix of sampled values for parameter c_j of the Lasso distribution for each \beta_j.

• Modified_PC_Gibbs: returns a list containing:

  mBeta

  Matrix of MCMC samples for the regression coefficients \beta.

  vsigma2

  Vector of MCMC samples for the error variance \sigma^2.

  vlambda2

  Vector of MCMC samples for the shrinkage parameter \lambda^2.

  mM

  Matrix of estimated means of the full conditional distributions of each \beta_j.

  mV

  Matrix of estimated variances of the full conditional distributions of each \beta_j.

  va_til

  Vector of estimated shape parameters for the full conditional inverse-gamma distribution of \sigma^2.

  vb_til

  Vector of estimated rate parameters for the full conditional inverse-gamma distribution of \sigma^2.

  vu_til

  Vector of estimated shape parameters for the full conditional inverse-gamma distribution of \lambda^2.

  vv_til

  Vector of estimated rate parameters for the full conditional inverse-gamma distribution of \lambda^2.

See Also

normalize for preprocessing input data before applying the samplers.

Examples

a <- 2; b <- 1; c <- 3
x <- seq(-3, 3, length.out = 1000)
plot(x, dlasso(x, a, b, c, logarithm = FALSE), type = 'l')

r <- rlasso(1000, a, b, c)
hist(r, breaks = 50, probability = TRUE, col = "grey", border = "white")
lines(x, dlasso(x, a, b, c, logarithm = FALSE), col = "blue")

plasso(0, a, b, c)
qlasso(0.25, a, b, c)
elasso(a, b, c)
vlasso(a, b, c)
mlasso(a, b, c)
MillsRatio(2)




# The Modified_Hans_Gibbs() function uses the Lasso distribution to draw 
# samples from the full conditional distribution of the regression coefficients.

y <- 1:20
X <- matrix(c(1:20,12:31,7:26),20,3,byrow = TRUE)

a1 <- b1 <- u1 <- v1 <- 0.01
sigma2_init <- 1
lambda_init <- 0.1
beta_init <- rep(1, ncol(X))
nsamples <- 1000
verbose <- 100

Output_Hans <- Modified_Hans_Gibbs(
                X, y, a1, b1, u1, v1,
                nsamples, beta_init, lambda_init, sigma2_init, verbose
)

colMeans(Output_Hans$mBeta)
mean(Output_Hans$vlambda2)


Output_PC <- Modified_PC_Gibbs(
               X, y, a1, b1, u1, v1, 
               nsamples, lambda_init, sigma2_init, verbose)

colMeans(Output_PC$mBeta)
mean(Output_PC$vlambda2)

Normalize Response and Covariates

Description

This function centers and (optionally) scales the response vector and each column of the design matrix using the population variance. It is used to prepare data for Bayesian Lasso regression.

Usage

normalize(y, X, scale = TRUE)

Arguments

Value

A list with the following elements:

• vy: Normalized response vector.

• mX: Normalized design matrix.

• mu.y: Mean of the response vector.

• sigma2.y: Population variance of the response vector.

• mu.x: Vector of column means of X.

• sigma2.x: Vector of population variances for columns of X.

Examples

set.seed(1)
X <- matrix(rnorm(100 * 10), 100, 10)
beta <- c(2, -3, rep(0, 8))
y <- as.vector(X %*% beta + rnorm(100))
norm_result <- normalize(y, X)