Main function of the package. Fits a range of models introduced in the
package vignette BayesSUR.pdf. Returns an object of S3 class
BayesSUR. There are three options for the prior on the residual
covariance matrix (i.e., independent inverse-Gamma, inverse-Wishart and
hyper-inverse Wishart) and three options for the prior on the latent
indicator variable (i.e., independent Bernoulli, hotspot and Markov random
field). So there are nine models in total. See details for their combinations.
BayesSUR(
data = NULL,
Y,
X,
X_0 = NULL,
covariancePrior = "HIW",
gammaPrior = "hotspot",
betaPrior = "independent",
nIter = 10000,
burnin = 5000,
nChains = 2,
outFilePath = "",
gammaSampler = "bandit",
gammaInit = "R",
mrfG = NULL,
standardize = TRUE,
standardize.response = TRUE,
maxThreads = 1,
output_gamma = TRUE,
output_beta = TRUE,
output_Gy = TRUE,
output_sigmaRho = TRUE,
output_pi = TRUE,
output_tail = TRUE,
output_model_size = TRUE,
output_model_visit = FALSE,
output_CPO = FALSE,
output_Y = TRUE,
output_X = TRUE,
hyperpar = list(),
tmpFolder = "tmp/"
)An object of class BayesSUR is saved as
obj_BayesSUR.RData in the output file, including the following
components:
status - the running status
input - a list of all input parameters by the user
output - a list of the all output filenames:
"*_logP_out.txt" - contains each row for the \(1000t\)-th iteration's log-likelihoods of parameters, i.e., Tau, Eta, JunctionTree, SigmaRho, O, Pi, Gamma, W, Beta and data conditional log-likelihood depending on the models.
"*_gamma_out.txt" - posterior mean of the latent indicator matrix.
"*_pi_out.txt" - posterior mean of the predictor effects (prospensity) by decomposing the probability of the latent indicator.
"*_hotspot_tail_p_out.txt" - posterior mean of the hotspot tail probability. Only available for the hotspot prior on the gamma.
"*_beta_out.txt" - posterior mean of the coefficients matrix.
"*_Gy_out.txt" - posterior mean of the response graph. Only available for the HIW prior on the covariance.
"*_sigmaRho_out.txt" - posterior mean of the transformed parameters. Not available for the IG prior on the covariance.
"*_model_size_out.txt" - contains each row for the\(1000t\)-th iteration's model sizes of the multiple response variables.
"*_model_visit_gy_out.txt" - contains each row for the nonzero indices of the vectorized estimated graph matrix for each iteration.
"*_model_visit_gamma_out.txt" - contains each row for the nonzero indices of the vectorized estimated gamma matrix for each iteration.
"*_CPO_out.txt" - the (scaled) conditional predictive ordinates (CPO).
"*_CPOsumy_out.txt" - the (scaled) conditional predictive ordinates (CPO) with joint posterior predictive of the response variables.
"*_WAIC_out.txt" - the widely applicable information criterion (WAIC).
"*_Y.txt" - responses dataset.
"*_X.txt" - predictors dataset.
"*_X0.txt" - fixed predictors dataset.
call - the matched call.
a numeric matrix with variables on the columns and observations
on the rows, if arguments Y and X (and possibly X_0)
are vectors. Can be NULL if arguments Y and X (and
possibly X_0) are numeric matrices
vectors of indices (with respect to the data matrix) for the
outcomes (Y) and the predictors to select (X) respectively;
if the data argument is NULL, these needs to be numeric
matrices containing the data instead, with variables on the columns and
observations on the rows
vectors of indices (with respect to the data matrix) for the fixed predictors that are not selected, i.e. always included in the model; if the data argument is not provided, this needs to be a numeric matrix containing the data instead, with variables on the columns and observations on the rows
string indicating the prior for the covariance $C$;
it has to be either HIW for the hyper-inverse-Wishar (which will
result in a sparse covariance matrix), IW for the inverse-Wishart
prior (dense covariance) or IG for independent inverse-Gamma on all
the diagonal elements and 0 otherwise. See the details for the model
specification
string indicating the gamma prior to use, either
hotspot (default) for the Hotspot prior of Bottolo (2011), MRF
for the Markov Random Field prior or hierarchical for a simpler
hierarchical prior. See the details for the model specification
string indicating the prior for regression coefficients; it
has to be either independent for independent spike-and-slab priors
(only slab part for X_0 if specified), or reGroup for weakly
normal priors for mandatory variables (random effects) and spike-and-slab
priors for other variables of Zhao (2023)
number of iterations for the MCMC procedure. Default 10000
number of iterations to discard at the start of the chain. Default is 5000
number of parallel tempered chains to run (default 2). The temperature is adapted during the burnin phase
path to where the output files are to be written
string indicating the type of sampler for gamma, either
bandit for the Thompson sampling inspired samper or MC3 for
the usual MC^3 sampler. See Russo et al.(2018) or Madigan and York (1995)
for details
gamma initialisation to either all-zeros (0), all
ones (1), MLE-informed (MLE) or (default) randomly (R)
either a matrix or a path to the file containing (the edge list of) the G matrix for the MRF prior on gamma (if necessary)
logical flag for X variable standardization. Default is
standardize=TRUE. Coefficients are returned on the standardized scale
logical flag for Y standardization. Default is
standardize.response=TRUE
maximum threads used for parallelization. Default is 1.
Reproducibility of results with set.seed() is only guaranteed if
maxThreads=1
allow (TRUE) or suppress (FALSE) the
output for gamma. See the return value below for more information
allow (TRUE) or suppress (FALSE) the output
for beta. See the return value below for more information
allow (TRUE) or suppress (FALSE) the output
for Gy. See the return value below for more information
allow (TRUE) or suppress (FALSE) the
output for sigmaRho. See the return value below for more information
allow (TRUE) or suppress (FALSE) the output
for pi. See the return value below for more information
allow (TRUE) or suppress (FALSE) the output
for tail (hotspot tail probability). See the return value below for more
information
allow (TRUE) or suppress (FALSE) the
output for model_size. See the return value below for more information
allow (TRUE) or suppress (FALSE) the
output for all visited models over the MCMC iterations. Default is
FALSE. See the return value below for more information
allow (TRUE) or suppress (FALSE) the output
for (scaled) conditional predictive ordinates (*_CPO_out.txt),
CPO with joint posterior predictive of the response variables
(*_CPOsumy_out.txt) and widely applicable information criterion
(*_WAIC_out.txt). See the return value below for more information
allow (TRUE) or suppress (FALSE) the output
for responses dataset Y
allow (TRUE) or suppress (FALSE) the output
for predictors dataset X
a list of named hypeparameters to use instead of the default values. Valid names are mrf_d, mrf_e, a_sigma, b_sigma, a_tau, b_tau, nu, a_eta, b_eta, a_o, b_o, a_pi, b_pi, a_w and b_w. Their default values are a_w=2, b_w=5, a_omega=2, b_omega=1, a_o=2, b_o=p-2, a_pi=2, b_pi=1, nu=s+2, a_tau=0.1, b_tau=10, a_eta=0.1, b_eta=1, a_sigma=1, b_sigma=1, mrf_d=-3 and mrf_e=0.03. See the vignette for more information
the path to a temporary folder where intermediate data
files are stored (will be erased at the end of the chain). It is specified
relative to outFilePath
The arguments covariancePrior and gammaPrior specify
the model HRR, dSUR or SSUR with different gamma prior. Let
\(\gamma_{jk}\) be latent indicator variable of each coefficient and
\(C\) be covariance matrix of response variables. The nine models
specified through the arguments covariancePrior and
gammaPrior are as follows.
| \(\gamma_{jk}\)~Bernoulli | \(\gamma_{jk}\)~hotspot | \(\gamma\)~MRF | |
| \(C\)~indep | HRR-B | HRR-H | HRR-M |
| \(C\)~IW | dSUR-B | dSUR-H | dSUR-M |
| \(C\)~HIW | SSUR-B | SSUR-H | SSUR-M |
Russo D, Van Roy B, Kazerouni A, Osband I, Wen Z (2018). A tutorial on Thompson sampling. Foundations and Trends in Machine Learning, 11: 1-96.
Madigan D, York J (1995). Bayesian graphical models for discrete data. International Statistical Review, 63: 215–232.
Bottolo L, Banterle M, Richardson S, Ala-Korpela M, Jarvelin MR, Lewin A (2020). A computationally efficient Bayesian seemingly unrelated regressions model for high-dimensional quantitative trait loci discovery. Journal of Royal Statistical Society: Series C, 70: 886-908.
Zhao Z, Banterle M, Bottolo L, Richardson S, Lewin A, Zucknick M (2021). BayesSUR: An R package for high-dimensional multivariate Bayesian variable and covariance selection in linear regression. Journal of Statistical Software, 100: 1–32.
Zhao Z, Banterle M, Lewin A, Zucknick M (2023). Multivariate Bayesian structured variable selection for pharmacogenomic studies. Journal of the Royal Statistical Society: Series C (Applied Statistics), qlad102.
data("exampleEQTL", package = "BayesSUR")
hyperpar <- list(a_w = 2, b_w = 5)
set.seed(9173)
fit <- BayesSUR(
Y = exampleEQTL[["blockList"]][[1]],
X = exampleEQTL[["blockList"]][[2]],
data = exampleEQTL[["data"]], outFilePath = tempdir(),
nIter = 5, burnin = 0, nChains = 1, gammaPrior = "hotspot",
hyperpar = hyperpar, tmpFolder = "tmp/", output_CPO = TRUE
)
## check output
# show the summary information
summary(fit)
# show the estimated beta, gamma and graph of responses Gy
plot(fit, estimator = c("beta", "gamma", "Gy"), type = "heatmap")
if (FALSE) {
## Set up temporary work directory for saving a pdf figure
# td <- tempdir()
# oldwd <- getwd()
# setwd(td)
## Produce authentic math formulas in the graph
# plot(fit, estimator = c("beta", "gamma", "Gy"), type = "heatmap", fig.tex = TRUE)
# system(paste(getOption("pdfviewer"), "ParamEstimator.pdf"))
# setwd(oldwd)
}
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