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含协变量的有向网络模型中的统计推断AI 解读

Ting Yana http://orcid.org/0000-0001-9830-6646, Binyan Jiangb, Stephen E. Fienbergc* & Chenlei Lengd*a Department of Statistics, Central China Normal University, Wuhan, Chinab Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, Chinac Department of Statistics, Heinz College, Machine Learning Department, Cylab, Carnegie Mellon University, Pittsburgh, PAd Department of Statistics, University of Warwick and Alan Turing Institute, Coventry, UKCONTACT…

图式记录链接与去重的贝叶斯方法AI 解读

We propose an unsupervised approach for linking records across arbitrarily many files, while simultaneously detecting duplicate records within files. Our key innovation involves the representation of the pattern of links between records as a bipartite graph, in which records are directly linked to latent true individuals, and only indirectly linked to other records. This flexible representation of the linkage structure naturally allows us to estimate the attributes of the…

β 模型中的最大似然估计AI 解读

We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based on the polytope of degree sequences, for the existence of the maximum likelihood estimator (MLE) of the model parameters. We characterize in a combinatorial fashion sample points leading to a nonexistent MLE, and nonestimability of the…

多文件记录链接的广义Fellegi–Sunter框架及凶杀记录应用AI 解读

We present a probabilistic method for linking multiple datafiles. This task is not trivial in the absence of unique identifiers for the individuals recorded. This is a common scenario when linking census data to coverage measurement surveys for census coverage evaluation, and in general when multiple record systems need to be integrated for posterior analysis. Our method generalizes the Fellegi–Sunter theory for linking records from two datafiles and its modern…

对数线性模型中的最大似然估计AI 解读

We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and investigate estimability of the natural and mean-value parameters under a nonexistent MLE. Our conditions focus on the role of sampling zeros in the observed table. We situate our results within the framework of extended exponential families,…

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条件对数线性结构的合并AI 解读

Graphical models offer simple and intuitive interpretations in terms of conditional independence relationships, and these are especially valuable when large numbers of variables are involved. In some settings, restrictions on experiments and other forms of data collection may result in our being able to estimate only parts of a large graphical model; for example, when the data in a large contingency table are extremely sparse. In other settings, we might use a model building…

条件对数线性结构的组合AI 解读

Graphical models offer simple and intuitive interpretations in terms of conditional independence relationships, and these are especially valuable when large numbers of variables are involved. In some settings, restrictions on experiments and other forms of data collection may result in our being able to estimate only parts of a large graphical model; for example, when the data in a large contingency table are extremely sparse. In other settings, we might use a model building…

捕获概率异质性下人口估计的三样本多重再捕获方法AI 解读

A central assumption in the standard capture-recapture approach to the estimation of the size of a closed population is the homogeneity of the “capture” probabilities. In this article we develop an approach that allows for varying susceptibility to capture through individual parameters using a variant of the Rasch model from psychological measurement situations. Our approach requires an additional recapture. In the context of census undercount estimation, this requirement…

多重社会关系的统计分析AI 解读

Loglinear models are adapted for the analysis of multivariate social networks, a set of sociometric relations among a group of actors. Models that focus on the similarities and differences between the relations and models that concentrate on individual actors are discussed. This approach allows for the partitioning of the actors into blocks or subgroups. Some ideas for combining these models are described, and the various models and computational methods are applied to the…

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分类数据问题中卡方统计量的使用AI 解读

Summary The use of χ2 statistics for categorical data problems was initiated by Karl Pearson, but it took several years before the asymptotic distribution of these statistics was well understood. The general structure of asymptotic results for χ2 statistics is reviewed and the applicability of the general structure to a variety of problems of practical interest is discussed. These problems include the use of χ2 statistics in small-sample situations and in large sparse…

会计总体中总高估误差的估计AI 解读

Auditors wishing to estimate the total amount of errors in a set of accounts have tended to use estimation procedures which rely on approximate normality for large sample sizes. Since this reliance is often not well-founded for sample sizes used in auditing practice, efforts have been made to circumvent this difficulty. This paper will briefly describe these efforts and then present a new approach based on the multinomial probability distribution which yields confidence…

成对与多项比较模型的对数线性表示AI 解读

This paper develops log linear model representations for the Bradley-Terry paired comparisons and Luce multiple comparisons models. Various multivariate extensions of the Bradley-Terry model are then considered. A model is presented, similar to one of Davidson & Bradley (1969), but which is based on the log odds ratio as a measure of association rather than the ø coefficient of correlation. It is shown that, by the adaptive use of log linear model theory, complex data seta…

成对比较与多项比较模型的对数线性表示AI 解读

SUMAIARY This paper develops log linear model representations for the Bradley-Terry paired comparisons and Luce multiple comparisons models. Various multivariate extensions of the Bradley-Terry model are then considered. A model is presented, similar to one of Davidson & Bradley (1969), but which is based on the log odds ratio as a measure of association rather than the 0 coefficient of correlation. It is shown that, by the adaptive use of log linear model theory, complex…

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多项分布单元概率的同时估计AI 解读

A new estimator, p*, of the multinomial parameter vector is proposed, and it is shown to be a better choice in most situations than the usual estimator, (the vector of observed proportions). The risk functions (expected squared-error loss) of these two estimators are examined in three ways using: (a) exact calculations, (b) standard asymptotic theory, and (c) a novel asymptotic framework in which the number of cells is large and the number of observations per cell is…

封闭总体的多次重捕普查与不完全列联表AI 解读

The multiple recapture census for closed populations is reconsidered, assuming an underlying multinomial sampling model. The resulting data can be put in the form of an incomplete 2k contingency table, with one missing cell, that displays the full multiple recapture history of all individuals in the population. Log linear models are fitted to this incomplete contingency table, and the simplest plausible model that fits the observed cells is projected to cover the miming…

不完整列联表中的准独立性与最大似然估计AI 解读

Many authors have been concerned with contingency tables containing cells which are missing, a priori zero or otherwise specified. This article examines the problem of maximum likelihood estimation for such tables under the “quasi-in-dependence” model. In particular, conditions are provided to ensure the existence of unique nonzero maximum likelihood estimates for the cells of incomplete tables obtained by deleting the missing or a priori zero cells, even when other cells…

不完整列联表中的准独立性与最大似然估计AI 解读

Many authors have been concerned with contingency tables containing cells which are missing, a priori zero or otherwise specified. This article examines the problem of maximum likelihood estimation for such tables under the “quasi-in-dependence” model. In particular, conditions are provided to ensure the existence of unique nonzero maximum likelihood estimates for the cells of incomplete tables obtained by deleting the missing or a priori zero cells, even when other cells…