R: Fitting BayesSUR models

BayesSUR {BayesSUR}

R Documentation

Fitting BayesSUR models

Description

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.

Usage

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,
  tick = 1000,
  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/"
)

Arguments

`data`	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
`Y`, `X`	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
`X_0`	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
`covariancePrior`	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
`gammaPrior`	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
`betaPrior`	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)
`nIter`	number of iterations for the MCMC procedure. Default 10000
`burnin`	number of iterations to discard at the start of the chain. Default is 5000
`nChains`	number of parallel tempered chains to run (default 2). The temperature is adapted during the burnin phase
`outFilePath`	path to where the output files are to be written
`gammaSampler`	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
`gammaInit`	gamma initialisation to either all-zeros (`0`), all ones (`1`), MLE-informed (`MLE`) or (default) randomly (`R`)
`mrfG`	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)
`standardize`	logical flag for X variable standardization. Default is `standardize=TRUE`. Coefficients are returned on the standardized scale
`standardize.response`	logical flag for Y standardization. Default is `standardize.response=TRUE`
`maxThreads`	maximum threads used for parallelization. Default is 1. Reproducibility of results with `set.seed()` is only guaranteed if `maxThreads=1`
`tick`	an integer used for printing the iteration index and some updated parameters every tick-th iteration. Default is 1000
`output_gamma`	allow (`TRUE`) or suppress (`FALSE`) the output for gamma. See the return value below for more information
`output_beta`	allow (`TRUE`) or suppress (`FALSE`) the output for beta. See the return value below for more information
`output_Gy`	allow (`TRUE`) or suppress (`FALSE`) the output for Gy. See the return value below for more information
`output_sigmaRho`	allow (`TRUE`) or suppress (`FALSE`) the output for sigmaRho. See the return value below for more information
`output_pi`	allow (`TRUE`) or suppress (`FALSE`) the output for pi. See the return value below for more information
`output_tail`	allow (`TRUE`) or suppress (`FALSE`) the output for tail (hotspot tail probability). See the return value below for more information
`output_model_size`	allow (`TRUE`) or suppress (`FALSE`) the output for model_size. See the return value below for more information
`output_model_visit`	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
`output_CPO`	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
`output_Y`	allow (`TRUE`) or suppress (`FALSE`) the output for responses dataset Y
`output_X`	allow (`TRUE`) or suppress (`FALSE`) the output for predictors dataset X
`hyperpar`	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
`tmpFolder`	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`

Details

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

Value

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 the1000t-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.

References

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.

Examples

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")

## Not run: 
## 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)

## End(Not run)

[Package BayesSUR version 2.1-7 Index]