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分类变量随机有序分布的贝叶斯分析AI 解读

This article considers a finite set of discrete distributions all having the same finite support. The problem of interest is to assess the strength of evidence produced by sampled data for a hypothesis of a specified stochastic ordering among the underlying distributions and to estimate these distributions subject to the ordering. We present a Bayesian approach that is an alternative to using the posterior probability of the hypothesis and the Bayes factor in favor of the…

方差分量模型的贝叶斯方法AI 解读

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the…

方差分量模型的贝叶斯方法AI 解读

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the…

线性模型异常值检测概率方法的比较AI 解读

This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived.

二维列联表潜类别分析的贝叶斯方法AI 解读

Latent class analysis in two-way contingency tables usually suffers from unidentifiability problems. These an be overcome by using Bayesian techniques in which prior distributions are assumed on the latent parameters. Application of these techniques, however, involves some unusual computational difficulties. Bayesian techniques suitable for latent class analyses together with a remedy to the computational difficulties are discussed in this paper.

二维列联表潜类别分析的贝叶斯方法AI 解读

Latent class analysis in two-way contingency tables usually suffers from unidentifiability problems. These an be overcome by using Bayesian techniques in which prior distributions are assumed on the latent parameters. Application of these techniques, however, involves some unusual computational difficulties. Bayesian techniques suitable for latent class analyses together with a remedy to the computational difficulties are discussed in this paper.

响应变量存在缺失观测的多元回归贝叶斯推断AI 解读

We discuss the case of the multivariate linear model Y = XB + E with Y an (n × p) matrix, and so on, when there are missing observations in the Y matrix in a so-called nested pattern. We propose an analysis that arises by incorporating the predictive density of the missing observations in determining the posterior distribution of B, and its mean and variance matrix. This involves us with matric-T variables. The resulting analysis is illustrated with some Canadian economic…

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Villegas 确定先验分布方法中的不一致性AI 解读

A recent paper by Villegas (1969) uses a fiducial type argument to lend support to the use of Jeffrey's invariant prior for the variance-covariance matrix in the non-informative situation. Sampling is assumed to be on a multi-normal random variable. Villegas proceeds by selecting a pivotal quantity which has a fixed distribution. Since there is nothing unique about this pivotal quantity, we note in this paper, that the Villegas fiducial approach could lead to other priors,…

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在拟合优度问题中使用未来观测的概念AI 解读

Summary An attack on the problem of goodness of fit is made by combining a Bayesian and sampling argument; the Bayesian part is effected by using the distribution of a future observation, while the sampling argument concerns itself with the distribution of a “chi-squared like” statistic, which measures discrepancies of observed frequencies from those predicted by the distribution of the future observation. Examples are given for the case of sampling from the binomial,…

固定效应单因素方差分析中组间方差不等的贝叶斯视角AI 解读

Abstract : The effect of inequality of variance on the standard F-tests for one-way and two-way analysis of variance classification has been examined previously. Certain results found by Box for the one-way classification are examined. A Bayesian analysis is shown to throw light on the consequences of Box's work in a given experimental situation.

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