adaBridge: Adaptive Bayesian Bridge Regression

In abnormally-distributed/Bayezilla: Bayesian Models With JAGS and Several Utilities for Data Exploration and Model Evaluation.

Description

The Bayesian Bridge model of Mallick & Yi (2018) combined with the Adaptive Bayesian LASSO of Leng, Tran and David Nott (2018). Bridge regression allows you to utilize different Lp norms for the shape of the prior through the shape parameter kappa of the power exponential distribution (also known as generalized Gaussian). Norms of 1 and 2 give the Laplace and Gaussian distributions respectively (corresponding to the LASSO and Ridge Regression). Norms smaller than 1 are very difficult to estimate directly, but have very tall modes at zero and very long, cauchy like tails. Values greater than 2 become increasingly platykurtic, with the uniform distribution arising as it approaches infinity.

The individual lambdas on each parameter defined by a gamma(sh, ra) distribution, where sh and ra are shape and rate hyperparameters. Here sh and ra are given gamma(4, 8) and gamma(1, 5) priors respectively. This places the expected values for the shape and rate parameters at 0.50 and 0.20 respectively, which is consistent with the gamma(0.50, 0.20) prior on lambda used for most other shrinkage models in this package

JAGS has no built in power exponential distribution, so the distribution is parameterized as a uniform-gamma mixture just as in Mallick & Yi (2018). The parameterization is given below. For generalized linear models plug-in pseudovariances are used.

Model Specification:



Plugin Pseudo-Variances:

Usage

adaBridge(formula, data, family = "gaussian", kappa = 1.4,
  log_lik = FALSE, iter = 10000, warmup = 1000, adapt = 2000,
  chains = 4, thin = 1, method = "parallel", cl = makeCluster(2),
  ...)

Arguments

formula	the model formula
data	a data frame.
family	one of "gaussian", "binomial", or "poisson".
kappa	the Lp norm you wish to utilize. Default is 1.4.
log_lik	Should the log likelihood be monitored? The default is FALSE.
iter	How many post-warmup samples? Defaults to 10000.
warmup	How many warmup samples? Defaults to 1000.
adapt	How many adaptation steps? Defaults to 2000.
chains	How many chains? Defaults to 4.
thin	Thinning interval. Defaults to 1.
method	Defaults to "parallel". For an alternative parallel option, choose "rjparallel" or. Otherwise, "rjags" (single core run).
cl	Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. Defaults to two cores.
...	Other arguments to run.jags.

Value

a runjags object

References

Leng, C., Tran, M.N., & Nott, D.J. (2014). Bayesian adaptive Lasso. arXiv:1009.2300

Mallick, H. & Yi, N. (2018) Bayesian bridge regression, Journal of Applied Statistics, 45:6, 988-1008, DOI: 10.1080/02664763.2017.1324565

Examples

adaBridge()

abnormally-distributed/Bayezilla documentation built on Oct. 31, 2019, 1:57 a.m.