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随机分布及相关函数的贝叶斯非参数推断AI 解读

Summary In recent years, Bayesian nonparametric inference, both theoretical and computational, has witnessed considerable advances. However, these advances have not received a full critical and comparative analysis of their scope, impact and limitations in statistical modelling; many aspects of the theory and methods remain a mystery to practitioners and many open questions remain. In this paper, we discuss and illustrate the rich modelling and analytic possibilities that…

无限可分分布的近似随机数生成及其贝叶斯推断应用AI 解读

SUMMARY Stochastic processes with independent increments play a central role in Bayesian nonparametric inference. The distributions of the increments of these processes, aside from fixed points of discontinuity, are infinitely divisible and their Laplace and/or Fourier transforms in the Lévy representation are usually known. Conventional Bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest, although…

预测式模型选择AI 解读

SUMMARY We consider the problem of selecting one model from a large class of plausible models. A predictive Bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model. Using criteria derived from a certain predictive density and a prior specification that emphasizes the observables, we implement the proposed methodology for three common problems arising in normal…

设计实验分析的预测方法AI 解读

Viewing the analysis of designed experiments as a model selection problem, we introduce the use of a predictive Bayesian criterion in this context based on the predictive density of a replicate experiment (PDRE). A calibration of the criterion is provided to assist in the model choice. The relationships of the proposed criterion to other prevalent criteria, such as AIC, BIC, and Mallows's C p , are given. An information theoretic criterion based on the PDRE's of two…

使用 Jeffreys 先验的广义线性模型贝叶斯分析AI 解读

Generalized linear models (GLM's) have proved suitable for modeling various kinds of data consisting of exponential family response variables with covariates. Bayesian analysis of such data requires specification of a prior for the regression parameters in the model used. Uniform priors are very commonly used as conventional noninformative priors. We show, however, that uniform priors for GLM's can lead to improper posterior distributions thus making them undesirable.…