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结构化收缩：回归中的相关先验AI 解读

This paper develops a rich class of sparsity priors for regression effects that encourage shrinkage of both regression effects and contrasts between effects to zero whilst leaving sizeable real effects largely unshrunk. The construction of these priors uses some properties of normal-gamma distributions to include design features in the prior specification, but has general relevance to any continuous sparsity prior. Specific prior distributions are developed for serial…

结合回归变量选择的贝叶斯模型平均AI 解读

Summary When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly…

多变量判别分析AI 解读

Many statistical methods for discriminant analysis do not adapt well or easily to situations where the number of variables is large, possibly even exceeding the number of cases in the training set. We explore a variety of methods for providing robust identification of future samples in this situation. We develop a range of flexible Bayesian methods, and primarily a new hierarchical covariance compromise method, akin to regularized discriminant analysis. Although the methods…

多元贝叶斯变量选择与预测AI 解读

Summary The multivariate regression model is considered with p regressors. A latent vector with p binary entries serves to identify one of two types of regression coefficients: those close to 0 and those not. Specializing our general distributional setting to the linear model with Gaussian errors and using natural conjugate prior distributions, we derive the marginal posterior distribution of the binary latent vector. Fast algorithms aid its direct computation, and in high…

多元校准AI 解读

Summary A set of q responses Y = (Y 1 ,…, Yq)T are determined by a set of p explanatory variables x = (X 1,…, Xp)T. A set of l observed vectors Y are available at a single unknown x and it is desired to draw inferences about this unknown vector X. In order to do this calibrating data is available jointly on (Y, X) where two situations are distinguished (i), x is controlled, (ii) x is random. Using orthodox sampling theory on the one hand and Bayesian methods on the other…

自适应多元岭回归AI 解读

A multivariate version of the Hoerl-Kennard ridge regression rule is introduced. The choice from among a large class of possible generalizations is guided by Bayesian considerations; the result is implicitly in the work of Lindley and Smith although not actually derived there. The proposed rule, in a variety of equivalent forms is discussed and the choice of its ridge matrix considered. As well, adaptive multivariate ridge rules and closely related empirical Bayes procedures…