相关论文: Block Hyper-g Priors in Bayesian Regression

Mixtures of Zellner's g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to Generalized…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

The Zellner's g-prior and its recent hierarchical extensions are the most popular default prior choices in the Bayesian variable selection context. These prior set-ups can be expressed power-priors with fixed set of imaginary data. In this…

Zellner's $g$-prior is a popular prior choice for the model selection problems in the context of normal regression models. Wang and Sun [J. Statist. Plann. Inference 147 (2014) 95-105] recently adopt this prior and put a special hyper-prior…

In the Bayesian stochastic search variable selection framework, a common prior distribution for the regression coefficients is the g-prior of Zellner (1986). However, there are two standard cases in which the associated covariance matrix…

In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to…

This paper introduces Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of $g$ priors that allow for differential shrinkage for various…

We propose that Bayesian variable selection for linear parametrisations with Gaussian iid likelihoods be based on the spherical symmetry of the diagonalised parameter space. Our r-prior results in closed forms for the evidence for four…

One of the main approaches used to construct prior distributions for objective Bayes methods is the concept of random imaginary observations. Under this setup, the expected-posterior prior (EPP) offers several advantages, among which it has…

In the context of the expected-posterior prior (EPP) approach to Bayesian variable selection in linear models, we combine ideas from power-prior and unit-information-prior methodologies to simultaneously produce a minimally-informative…

Consider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

Many regularization priors for Bayesian regression assume the regression coefficients are a priori independent. In particular this is the case for standard Bayesian treatments of the lasso and the elastic net. While independence may be…

We examine necessary and sufficient conditions for posterior consistency under $g$-priors, including extensions to hierarchical and empirical Bayesian models. The key features of this article are that we allow the number of regressors to…

Choosing the number of mixture components remains an elusive challenge. Model selection criteria can be either overly liberal or conservative and return poorly-separated components of limited practical use. We formalize non-local priors…

For the normal linear model variable selection problem, we propose selection criteria based on a fully Bayes formulation with a generalization of Zellner's $g$-prior which allows for $p>n$. A special case of the prior formulation is seen to…

It is well-known that the distribution over functions induced through a zero-mean iid prior distribution over the parameters of a multi-layer perceptron (MLP) converges to a Gaussian process (GP), under mild conditions. We extend this…

This paper studies Bayesian variable selection in linear models with general spherically symmetric error distributions. We propose sub-harmonic priors which arise as a class of mixtures of Zellner's g-priors for which the Bayes factors are…

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…