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扩展条件独立及其在因果推断中的应用AI 解读

The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions the calculus that applies for the two cases separately (axioms of a separoid) still applies for the extended case. These results provide a rigorous basis for a wide range of statistical concepts, including ancillarity and sufficiency, and,…

随机机制交互作用AI 解读

We define mechanistic interaction between the effects of two variables on an outcome in terms of departure of these effects from a generalized noisy-OR model in a stratum of the population. We develop a fully probabilistic framework for the observational identification of this type of interaction via excess risk or superadditivity, one novel feature of which is its applicability when the interacting variables have been generated by arbitrarily dichotomizing continuous…

贝叶斯模型不确定性中的结构马尔可夫图分布AI 解读

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [ Ann. Statist. 21 (1993) 1272–1317], which we term structural Markov properties, for both undirected decomposable and directed acyclic graphs, which requires that the structure of distinct components of the graph be conditionally independent given the existence of a separating component. This allows the analysis…

博弈论、最大熵、最小差异与稳健贝叶斯决策理论AI 解读

We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium theory of zero-sum games between Decision Maker and Nature, these two problems are shown to be dual to each other, the solution to each providing that to the other. Although Topsøe described this connection for the Shannon entropy over 20…

最优实验设计的一致性散布准则AI 解读

We characterize those coherent design criteria which depend only on the dispersion matrix (assumed proper and nonsingular) of the “state of nature,” which may be a parameter-vector or a set of future observables, and describe the associated decision problems. Connections are established with the classical approach to optimal design theory for the normal linear model, based on concave functions of the information matrix. Implications of the theory for more general models are…

论有效的点预测系统AI 解读

Summary Assume that a forecaster observes a sequence of random variables and issues predictions according to a point prediction systems, i.e. a rule which, at every time t, issues a point prediction for the next observation at time t+1. We introduce the concept of efficiency of a point prediction system, for the case that the joint distribution of the sequence of observations is known to belong to a parametric family, and performance is assessed by the long run sum of…

信任预测与半贝叶斯推断AI 解读

We investigate the problem of fiducial prediction for unobserved quantities within the framework of the functional model described previously by Dawid and Stone. It is supposed that these are related to a completely unknown parameter by means of a regular functional model, and that the observations are either given as known functions of the predictands, or are themselves related to them by means of a functional model. We develop algebraic conditions which allow the…

统计操作的条件独立理论AI 解读

A general calculus of conditional independence is developed, suitable for application to a wide range of statistical concepts such as sufficiency, parameter-identification, adequacy and ancillarity. A vehicle for this theory is the statistical operation, a structure-preserving map between statistical spaces. Concepts such as completeness and identifiability of mixtures arise naturally and play an important part. Some general theorems are exemplified by applications to…