论文检索

单调性的非参数贝叶斯检验AI 解读

This paper adopts a nonparametric Bayesian approach to testing whether a function is monotone. Two new families of tests are constructed. The first uses constrained smoothing splines with a hierarchical stochastic-process prior that explicitly controls the prior probability of monotonicity. The second uses regression splines together with two proposals for the prior over the regression coefficients. Via simulation, the finite-sample performance of the tests is shown to…

利用方差—均值混合进行非高斯回归的数据增广AI 解读

We use the theory of normal variance-mean mixtures to derive a data-augmentation scheme for a class of common regularization problems. This generalizes existing theory on normal variance mixtures for priors in regression and classification. It also allows variants of the expectation-maximization algorithm to be brought to bear on a wider range of models than previously appreciated. We demonstrate the method on several examples, focusing on the case of binary logistic…

稀疏信号的马蹄估计量AI 解读

This paper proposes a new approach to sparsity, called the horseshoe estimator, which arises from a prior based on multivariate-normal scale mixtures. We describe the estimator’s advantages over existing approaches, including its robustness, adaptivity to different sparsity patterns and analytical tractability. We prove two theorems: one that characterizes the horseshoe estimator’s tail robustness and the other that demonstrates a super-efficient rate of convergence to the…

高斯图模型中的客观贝叶斯模型选择AI 解读

This paper presents a default model-selection procedure for Gaussian graphical models that involves two new developments. First, we develop a default version of the hyper-inverse Wishart prior for restricted covariance matrices, called the hyper-inverse Wishart g-prior, and show how it corresponds to the implied fractional prior for selecting a graph using fractional Bayes factors. Second, we apply a class of priors that automatically handles the problem of multiple…