Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. " Prior elicitation, variable selection and Bayesian computation for logistic regression models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. " Nonlocal Priors for High-Dimensional Estimation,"
" GA: A Package for Genetic Algorithms in R," Journal of the American Statistical Association, American Statistical Association, vol. " Properties and Implementation of Jeffreys’s Prior in Binomial Regression Models," " Regularization Paths for Generalized Linear Models via Coordinate Descent," & Hastie, Trevor & Tibshirani, Rob, 2010. " Bayesian Subset Modeling for High-Dimensional Generalized Linear Models," Faming Liang & Qifan Song & Kai Yu, 2013." Bayesian Model Selection in High-Dimensional Settings," Finally, we illustrate the application of our methods with an analysis of the Pima Indians diabetes dataset. Furthermore, the simulation studies show that our methods lead to mean posterior probabilities for the true models that are closer to their empirical success rates. Simulation studies that consider binomial, Poisson, and negative binomial regression models indicate that our methods select true models with higher success rates than other existing Bayesian methods. We also show that, when compared to local priors, our hyper nonlocal priors lead to faster accumulation of evidence in favor of a true null hypothesis. We develop a Laplace integration procedure to compute posterior model probabilities, and we show that under certain regularity conditions the proposed methods are variable selection consistent. As a consequence, the hyper nonlocal priors bring less information on the effect sizes than the Fisher information priors, and thus are very useful in practice whenever the prior knowledge of effect size is lacking. We then obtain our hyper nonlocal priors from our nonlocal Fisher information priors by assigning hyperpriors to their scale parameters. To obtain these priors, we first derive two new priors for generalized linear models that combine the Fisher information matrix with the Johnson-Rossell moment and inverse moment priors.
We propose two novel hyper nonlocal priors for variable selection in generalized linear models.
0 kommentar(er)
