Pathway crosstalk effects: shrinkage and disentanglement using a Bayesian hierarchical model

Hierarchical priors for Bayesian CART shrinkage

The Bayesian CART (classiication and regression tree) approach proposed by Chipman, George and McCulloch (1998) entails putting a prior distribution on the set of all CART models and then using stochastic search to select a model. The main thrust of this paper is to propose a new class of hierarchical priors which enhance the potential of this Bayesian approach. These priors indicate a preferen...

Defining and Testing Diagnostic Equivalence Using a Bayesian Hierarchical Model

Adaptive Bayesian Shrinkage Estimation Using Log-Scale Shrinkage Priors

Global-local shrinkage hierarchies are an important, recent innovation in Bayesian estimation of regression models. In this paper we propose to use log-scale distributions as a basis for generating familes of flexible prior distributions for the local shrinkage hyperparameters within such hierarchies. An important property of the log-scale priors is that by varying the scale parameter one may v...

Bayesian shrinkage

Penalized regression methods, such as L1 regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through two-component mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimension...

Inferring regulatory networks using a hierarchical Bayesian graphical Gaussian model

In this paper, we propose a new formalism based on graphical Gaussian model (GGM) to infer genetic regulatory networks. A hierarchical Bayesian prior for the precision matrix of the GGM is introduced to impose a bias toward sparse graph structure. We show that the MAP estimation of the undirected graph can be readily obtained by a variant of the well-known Lasso regression algorithm. Then we in...