bats_map: Bayesian Adaptive T-Shrinkage Regression

In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description

This implements the block-updating expectation maximization algorithm presented in Mutshinda & Sillanpää (2012) for a regression model with marginal student t priors for the coefficients, along with coefficient specific shrinkage. The model takes two hyperparameters: nu, which is the degrees of freedom for the priors, and eta, which is the squared inverse scale parameter for the student t priors. When nu is 1, the marginal priors are Cauchy densities, and as nu tends to infinity it results in Gaussian densities and yields a ridge regression estimator as a result. Eta results in greater shrinkage as it increases, as it controls the precision of the priors.

Usage

bats_map(formula, data, prior = NULL)

Arguments

formula	model formula
data	a data frame
nu	the degrees of freedom parameter for the student t priors. defaults to 3.
eta	the prior precision parameter for the student t priors. defaults to 4.
nval	the length of the sequence of candidate lambda values to try.
opt.crit	the criterion to maximize for finding the optimal lambda when a sequence is provided. defaults to the log posterior ("logPost") to act as a MAP estimator, but final prediction error ("fpe") is also an option.

Value

a penreg object

References

Mutshinda, C. M., & Sillanpää, M. J. (2012). Swift block-updating EM and pseudo-EM procedures for Bayesian shrinkage analysis of quantitative trait loci. Theoretical and Applied Genetics, 125(7), 1575–1587. doi:10.1007/s00122-012-1936-1

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.