blm_bc_hs {SeBR} | R Documentation |
Bayesian linear model with a Box-Cox transformation and a horseshoe prior
Description
MCMC sampling for Bayesian linear regression with 1) a (known or unknown) Box-Cox transformation and 2) a horseshoe prior for the (possibly high-dimensional) regression coefficients.
Usage
blm_bc_hs(
y,
X,
X_test = X,
lambda = NULL,
sample_lambda = TRUE,
only_theta = FALSE,
nsave = 1000,
nburn = 1000,
nskip = 0,
verbose = TRUE
)
Arguments
y |
|
X |
|
X_test |
|
lambda |
Box-Cox transformation; if NULL, estimate this parameter |
sample_lambda |
logical; if TRUE, sample lambda, otherwise use the fixed value of lambda above or the MLE (if lambda unspecified) |
only_theta |
logical; if TRUE, only return posterior draws of the regression coefficients (for speed) |
nsave |
number of MCMC iterations to save |
nburn |
number of MCMC iterations to discard |
nskip |
number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw |
verbose |
logical; if TRUE, print time remaining |
Details
This function provides fully Bayesian inference for a
transformed linear model via MCMC sampling. The transformation is
parametric from the Box-Cox family, which has one parameter lambda
.
That parameter may be fixed in advanced or learned from the data.
The horseshoe prior is especially useful for high-dimensional settings with
many (possibly correlated) covariates. This function
uses a fast Cholesky-forward/backward sampler when p < n
and the Bhattacharya et al. (<https://doi.org/10.1093/biomet/asw042>) sampler
when p > n
. Thus, the sampler can scale linear in n
(for fixed/small p
) or linear in p
(for fixed/small n
).
Value
a list with the following elements:
-
coefficients
the posterior mean of the regression coefficients -
fitted.values
the posterior predictive mean at the test pointsX_test
-
post_theta
:nsave x p
samples from the posterior distribution of the regression coefficients -
post_ypred
:nsave x n_test
samples from the posterior predictive distribution at test pointsX_test
-
post_g
:nsave
posterior samples of the transformation evaluated at the uniquey
values -
post_lambda
:nsave
posterior samples of lambda -
post_sigma
:nsave
posterior samples of sigma -
model
: the model fit (here,blm_bc_hs
)
as well as the arguments passed in.
Note
Box-Cox transformations may be useful in some cases, but
in general we recommend the nonparametric transformation in sblm_hs
.
An intercept is automatically added to X
and
X_test
. The coefficients reported do *not* include
this intercept parameter, since it is not identified
under more general transformation models (e.g., sblm_hs
).
Examples
# Simulate data from a transformed (sparse) linear model:
dat = simulate_tlm(n = 100, p = 50, g_type = 'step', prop_sig = 0.1)
y = dat$y; X = dat$X # training data
hist(y, breaks = 25) # marginal distribution
# Fit the Bayesian linear model with a Box-Cox transformation & a horseshoe prior:
fit = blm_bc_hs(y = y, X = X, verbose = FALSE)
names(fit) # what is returned