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《一类随机凸多面体的 Gibbs 采样器》讨论AI 解读

This very welcome article is a fascinating contribution to an important subject. Persistent questions about the lower and upper probabilities includeWhat does it do in simple problems?What does it ...

We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Pólya’s urn. We give closed form normalizing constants, a simple method of simulation from the posterior and a characterization along the lines of W. E. Johnson’s characterization of the Dirichlet prior.

表格统计分析的序贯蒙特卡洛方法AI 解读

We describe a sequential importance sampling (SIS) procedure for analyzing two-way zero–one or contingency tables with fixed marginal sums. An essential feature of the new method is that it samples the columns of the table progressively according to certain special distributions. Our method produces Monte Carlo samples that are remarkably close to the uniform distribution, enabling one to approximate closely the null distributions of various test statistics about these…

随机转移矩阵的比较及其在信息论、统计学、经济学与人口科学中的应用AI 解读

Part 1 Partial orderings among stochastic matrices, Joel E. Cohen et al: introduction notation and definitions generalizations of classical channel comparisons degradation is the same as increasing density Shannon's inclusion implies smaller capacity a simple case - matrices A and B haver only two columns open problems. Part 2 Divergence and contraction coefficients, Gh. Zbaganu: introduction, definitions and notations a generalization of an inequality of Dobrushin the…

条件分布抽样的代数算法AI 解读

We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include contingency tables, logistic regression, and spectral analysis of permutation data. The algorithms involve computations in polynomial rings using Gröbner bases.

谱分析的推广及其在排序数据中的应用AI 解读

An analog of the spectral analysis of time series is developed for data in general spaces. This is applied to data from an election in which 5738 people rank ordered five candidates. Group theoretic considerations offer an analysis of variance like decomposition which seems natural and fruitful. A variety of inferential tools are suggested. The spectral ideas are then extended to general homogeneous spaces such as the sphere.

二维列联表的独立性检验：卡方统计量的新解释AI 解读

The classical chi-square test for independence in a two-way contingency table often rejects the independence hypothesis at an extremely small significance level, particularly when the sample size is large. This paper proposes some alternative distributions to independence, to help interpret the $\chi^2$ statistic in such situations. The uniform alternative, in which every possible contingency table of the given dimension and sample size receives equal probability, leads to…

图形投影寻踪的渐近理论AI 解读

Mathematical tools are developed for describing low-dimensional projections of high-dimensional data. Theorems are given to show that under suitable conditions, most projections are approximately Gaussian.

指数族的共轭先验AI 解读

Let $X$ be a random vector distributed according to an exponential family with natural parameter $\theta \in \Theta$. We characterize conjugate prior measures on $\Theta$ through the property of linear posterior expectation of the mean parameter of $X : E\{E(X|\theta)|X = x\} = ax + b$. We also delineate which hyperparameters permit such conjugate priors to be proper.