We consider the Bayesian lasso for regression, which can be interpreted as an L1 norm regularization based on a Bayesian approach when the Laplace or doubleexponential prior distribution is placed on the regression coefficients. A crucial issue is an appropriate choice of the values of hyperparameters included in the prior distributions, which essentially control the sparsity in the estimated model. To choose the values of tuning parameters, we introduce a model selection criterion for evaluating a Bayesian predictive distribution for the Bayesian lasso. Numerical results are presented to illustrate the properties of our sparse Bayesian modeling procedure.
Sparse regression procedures that are typified by the lasso enable us to perform variable selection and parameter estimation simultaneously. However, the lasso does not give the estimate of error variance, and also the tuning parameter selection still remains an important issue. On the other hand, although the Bayesian lasso can determine the estimate of error variance and the value of a tuning parameter as some Bayesian point estimates, it is difficult to derive sparse solution for the estimates of regression coefficients. To overcome these drawbacks, we propose a MAP Bayesian lasso by using the Monte Carlo integration for the posterior approximation. Monte Carlo simulations and real data examples are conducted to examine the efficiency of the proposed procedure.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.