| Type: | Package |
| Title: | Approximate Bayesian Regularization for Parsimonious Estimates |
| Date: | 2026-06-10 |
| Version: | 0.3.0 |
| Author: | Joris Mulder [aut, cre], Diana Karimova [aut, ctb], Sara van Erp [ctb], Roger Leenders [ctb] |
| Maintainer: | Joris Mulder <j.mulder3@tilburguniversity.edu> |
| Description: | Approximate Bayesian regularization using Gaussian approximations. The input is a vector of estimates and a Gaussian error covariance matrix of the key parameters. Bayesian shrinkage is then applied to obtain parsimonious solutions. The method is described on Karimova, van Erp, Leenders, and Mulder (2025) <doi:10.1016/j.jmp.2025.102925>. Gibbs samplers are used for model fitting. The shrinkage priors that are supported are Gaussian (ridge) priors, Laplace (lasso) priors (Park and Casella, 2008 <doi:10.1198/016214508000000337>), and horseshoe priors (Carvalho, et al., 2010; <doi:10.1093/biomet/asq017>). These priors include an option for grouped regularization of different subsets of parameters (Meier et al., 2008; <doi:10.1111/j.1467-9868.2007.00627.x>). F priors are used for the penalty parameters lambda^2 (Mulder and Pericchi, 2018 <doi:10.1214/17-BA1092>). This correspond to half-Cauchy priors on lambda (Carvalho, Polson, Scott, 2010 <doi:10.1093/biomet/asq017>). |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Imports: | Rcpp, stats, extraDistr, CholWishart, matrixcalc, logspline |
| LinkingTo: | Rcpp, RcppArmadillo |
| Suggests: | tinytest |
| NeedsCompilation: | yes |
| Packaged: | 2026-06-10 18:19:03 UTC; jorismulder |
| Repository: | CRAN |
| Date/Publication: | 2026-06-10 18:40:02 UTC |
The (scaled) F Distribution
Description
Density and random generation for the F distribution with first degrees of freedom df1,
second degrees of freedom df2, and scale parameter beta.
Usage
dF(x, df1, df2, beta, log = FALSE)
rF(n, df1, df2, beta)
Arguments
x |
vector of quantities. |
df1 |
First degrees of freedom |
df2 |
Second degrees of freedom |
beta |
Scale parameter |
log |
logical; if TRUE, density is given as log(p). |
n |
number of draws |
Value
dF gives the probability density of the F distribution. rF gives random draws from the F distribution.
References
Mulder and Pericchi (2018). The Matrix-F Prior for Estimating and Testing Covariance Matrices. Bayesian Analysis, 13(4), 1193-1214. <https://doi.org/10.1214/17-BA1092>
Examples
draws_F <- rF(n=1e4, df1=2, df2=4, beta=1)
hist(draws_F,500,xlim=c(0,10),freq=FALSE)
seqx <- seq(0,10,length=1e5)
lines(seqx,dF(seqx, df1=2, df2=4, beta=1),col=2,lwd=2)
The matrix F Distribution
Description
Density and random generation for the matrix variate F distribution with first degrees
of freedom df1, second degrees of freedom df2, and scale matrix B.
Usage
dmvF(x, df1, df2, B, log = FALSE)
rmvF(n, df1, df2, B)
Arguments
x |
Positive definite matrix of quantities. |
df1 |
First degrees of freedom |
df2 |
Second degrees of freedom |
B |
Positive definite scale matrix |
log |
logical; if TRUE, density is given as log(p). |
n |
Number of draws |
Value
dmvF returns the probability density of the matrix F distribution.
rmvF returns a numeric array, say R, of dimension p \times p \times n, where each element
R[,,i] is a positive definite matrix, a realization of the matrix F distribution.
References
Mulder and Pericchi (2018). The Matrix-F Prior for Estimating and Testing Covariance Matrices. Bayesian Analysis, 13(4), 1193-1214. <https://doi.org/10.1214/17-BA1092>
Examples
set.seed(20180222)
draws_F <- rmvF(n=1, df1=2, df2=4, B=diag(2))
dmvF(draws_F[,,1], df1=2, df2=4, B=diag(2))
Fast Bayesian regularization using Gaussian approximations
Description
The shrinkem function can be used for regularizing a vector
of estimates using Bayesian shrinkage methods where the uncertainty of the estimates
are assumed to follow a Gaussian distribution.
Usage
shrinkem(
x,
Sigma,
type,
group,
iterations,
burnin,
store,
cred.level,
df1,
df2,
scale2,
lambda2.fixed,
lambda2,
nugget,
...
)
Arguments
x |
A vector of estimates. |
Sigma |
A covariance matrix capturing the uncertainty of the estimates (e.g., error covariance matrix). |
type |
A character string which specifies the type of regularization method is used. Currently, the types "ridge", "lasso", and "horseshoe", are supported. |
group |
A vector of integers denoting the group membership of the estimates, where each group receives a different global shrinkage parameter which is adapted to the observed data. |
iterations |
Number of posterior draws after burnin. Default = 5e4. |
burnin |
Number of posterior draws in burnin. Default = 1e3. |
store |
Store every store-th draw from posterior. Default = 1 (implying that every draw is stored). |
cred.level |
The significance level that is used to check whether a parameter is nonzero depending on whether
0 is contained in the credible interval. The default is |
df1 |
First hyperparameter (degrees of freedom) of the prior for a shrinkage parameter lambda^2, which follows a F(df1,df2,scale2)
distribution. The default is |
df2 |
Second hyperparameter (degrees of freedom) of the prior for a shrinkage parameter lambda^2, which follows a F(df1,df2,scale2)
distribution. The default is |
scale2 |
Second hyperparameter (scale parameter) of the prior for a shrinkage parameter lambda^2, which follows a F(df1,df2,scale2)
distribution. The default is |
lambda2.fixed |
Logical indicating whether the penalty parameters(s) is/are fixed. Default is FALSE. |
lambda2 |
Positive scalars of length equal to the number of groups in 'group'. The argument is only used if the argument 'lambda2.fixed' is 'TRUE'. |
nugget |
A small positive value close to 0 which is used to avoid numerically singular matrices.
The default is |
... |
Parameters passed to and from other functions. |
Value
The output is an object of class shrinkem. The object has elements:
-
estimates: A data frame with the input estimates, the shrunken posterior mean, median, and mode, the lower and upperbound of the credbility interval based on the shrunken posterior, and a logical which indicates if zero is contained in the credibility interval. -
draws: List containing the posterior draws of the effects (beta), the prior parameters (tau2,gamma2), and the penalty parameters (psi2andlambda2). -
dim.est: The dimension of the input estimates ofbeta. -
input.est: The input vector of the unshrunken estimates ofbeta. -
call: Input call.
References
Karimovo, van Erp, Leenders, and Mulder (2024). Honey, I Shrunk the Irrelevant Effects! Simple and Fast Approximate Bayesian Regularization. <https://doi.org/10.31234/osf.io/2g8qm>
Examples
# EXAMPLE
estimates <- -5:5
covmatrix <- diag(11)
# Bayesian horseshoe where all beta's have the same global shrinkage
# (using default 'group' argument)
shrink1 <- shrinkem(estimates, covmatrix, type="horseshoe")
# posterior modes of middle three estimates are practically zero
# plot posterior densities
old.par.mfrow <- par(mfrow = c(1,1))
old.par.mar <- par(mar = c(0, 0, 0, 0))
par(mfrow = c(11,1))
par(mar = c(1,2,1,2))
for(p in 1:ncol(shrink1$draws$beta)){plot(density(shrink1$draws$beta[,p]),
xlim=c(-10,10),main=colnames(shrink1$draws$beta)[p])}
par(mfrow = old.par.mfrow)
par(mar = old.par.mar)
# Bayesian horseshoe where first three and last three beta's have different
# global shrinkage parameter than other beta's
shrink2 <- shrinkem(estimates, covmatrix, type="horseshoe",
group=c(rep(1,3),rep(2,5),rep(1,3)))
# posterior modes of middle five estimates are virtually zero
# plot posterior densities
par(mfrow = c(11,1))
par(mar = c(1,2,1,2))
for(p in 1:ncol(shrink2$draws$beta)){plot(density(shrink2$draws$beta[,p]),xlim=c(-10,10),
main=colnames(shrink2$draws$beta)[p])}
par(mfrow = old.par.mfrow)
par(mar = old.par.mar)