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二元工具变量模型的似然分析AI 解读

Instrumental variables are widely used for the identification of the causal effect of one random variable on another under unobserved confounding. The distribution of the observable variables for a discrete instrumental variable model satisfies certain inequalities but no conditional independence relations. Such models are usually tested by checking whether the relative frequency estimators of the parameters satisfy the constraints. This ignores sampling uncertainty in the…

用于最大化条件似然函数的 TM 算法AI 解读

This paper describes an algorithm for maximising a conditional likelihood function when the corresponding unconditional likelihood function is more easily maximised. The algorithm is similar to the EM algorithm but different as the parameters rather than the data are augmented and the conditional rather than the marginal likelihood function is maximised. In exponential families the algorithm takes a particular simple form which is computationally very close to the EM…

可分解图模型统计分析中的超 Markov 律AI 解读

This paper introduces and investigates the notion of a hyper Markov law, which is a probability distribution over the set of probability measures on a multivariate space that (i) is concentrated on the set of Markov probabilities over some decomposable graph, and (ii) satisfies certain conditional independence restrictions related to that graph. A stronger version of this hyper Markov property is also studied. Our analysis starts by reconsidering the properties of Markov…

定性与定量变量之间关联的图模型AI 解读

We define and investigate classes of statistical models for the analysis of associations between variables, some of which are qualitative and some quantitative. In the cases where only one kind of variables is present, the models are well-known models for either contingency tables or covariance structures. We characterize the subclass of decomposable models where the statistical theory is especially simple. All models can be represented by a graph with one vertex for each…

列联表的马尔可夫场与对数线性交互模型AI 解读

We use a close connection between the theory of Markov fields and that of log-linear interaction models for contingency tables to define and investigate a new class of models for such tables, graphical models. These models are hierarchical models that can be represented by a simple, undirected graph on as many vertices as the dimension of the corresponding table. Further all these models can be given an interpretation in terms of conditional independence and the…