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病例对照研究中似然与贝叶斯分析的回顾—前瞻对称性AI 解读

Prentice & Pyke (1979) established that the maximum likelihood estimate of an odds ratio in a case-control study is the same as would be found by fitting a logistic regression; in other words, for this specific target the incorrect prospective model is inferentially equivalent to the correct retrospective model.Similar results have been obtained for other models, and conditions have also been identified under which the corresponding Bayesian property holds, namely that the…

不依赖反事实的因果推断AI 解读

A popular approach to the framing and answering of causal questions relies on the idea of counterfactuals: Outcomes that would have been observed had the world developed differently; for example, if the patient had received a different treatment. By definition, one can never observe such quantities, nor assess empirically the validity of any modeling assumptions made about them, even though one's conclusions may be sensitive to these assumptions. Here I argue that for making…

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…

序贯概率预测有效性的检验AI 解读

Events are observed sequentially, and at each stage a probability for the next event is assessed. We consider the relationship between the sequence of probability forecasts and the sequence of outcomes. We argue that the forecasts may be considered “empirically valid” when both these sequences are consistent with a common joint distribution for the events. To aid in assessing validity, we introduce various test statistics that measure, in a natural way, the empirical…

似然与预序参照框架下的费舍尔推断AI 解读

SUMMARY In celebration of the centenary of the birth of Sir Ronald Fisher, this paper explores Fisher's conception of statistical inference, with special attention to the importance he placed on choosing an appropriate frame of reference to define the inferential model. In particular, we investigate inferential models which respect the likelihood principle or the prequential principle, and argue that these will typically have an asymptotic sampling theory justification.

基于校准的经验概率AI 解读

Probability forecasts for a sequence of uncertain events may be compared with the outcomes of those events by means of a natural criterion of empirical validity, calibration. It is shown that any two sequences of forecasts which both meet this criterion must be in asymptotic agreement. These agreed values can then be considered as correct objective probability forecasts for the particular sequence of outcome results obtained. However, the objective forecasts vary with the…

信赖推断的函数模型基础AI 解读

The role of functional models and their associated fiducial analysis is explored in an attempt to uncover a general theory of fiducial inference.

矩阵变量分布理论：记号考量与贝叶斯应用AI 解读

We introduce and justify a convenient notation for certain matrix-variate distributions which, by its emphasis on the important underlying parameters, and the theory on which it is based, eases greatly the task of manipulating such distributions. Important examples include the matrix-variate normal, t, F and beta, and the Wishart and inverse Wishart distributions. The theory is applied to compound matrix distributions and to Bayesian prediction in the multivariate linear…

We introduce and justify a convenient notation for certain matrix-variate distributions which, by its emphasis on the important underlying parameters, and the theory on which it is based, eases greatly the task of manipulating such distributions. Important examples include the matrix-variate normal, t, F and beta, and the Wishart and inverse Wishart distributions. The theory is applied to compound matrix distributions and to Bayesian prediction in the multivariate linear…

统计理论中的条件独立AI 解读

Summary Some simple heuristic properties of conditional independence are shown to form a conceptual framework for much of the theory of statistical inference. This framework is illustrated by an examination of the rôle of conditional independence in several diverse areas of the field of statistics. Topics covered include sufficiency and ancillarity, parameter identification, causal inference, prediction sufficiency, data selection mechanisms, invariant statistical models and…

若干涉及条件独立的误导性论证AI 解读

Summary Some misleading arguments in probability theory and statistics are examined, and shown to have a common structure, expressible in terms of conditional independence. Using an informal approach (which can be rigorized) the arguments are corrected by finding what conclusions are justified in general, and thus showing what further condition is needed to make the original arguments valid.

摘要暂缺

基于选择性报告数据的似然与贝叶斯推断AI 解读

If the reported data of an experiment have been subject to selection, then inference from such data should be modified accordingly. We investigate the modification required to the face-value likelihood. In particular, we derive conditions under which no modification is necessary and the data can be taken at face value.

不变分布与方差分析模型AI 解读

Subjective joint distributions over the outcomes of a set of possible observations, arising from a classical analysis of variance layout, are considered. These will often incorporate invariance properties associated with the symmetries of the layout. Then we show a formal equivalence with Bayesian multistage analysis of variance models. The invariance sheds further light on the analysis of such models. The argument is general, but is illustrated fully for the one-way layout.

不变分布与方差分析模型AI 解读

Subjective joint distributions over the outcomes of a set of possible observations, arising from a classical analysis of variance layout, are considered. These will often incorporate invariance properties associated with the symmetries of the layout. Then we show a formal equivalence with Bayesian multistage analysis of variance models. The invariance sheds further light on the analysis of such models. The argument is general, but is illustrated fully for the one-way layout.

球对称矩阵分布与多元线性模型AI 解读

Summary We consider inference about the parameters of a multivariate linear model, in which the usual assumption of normality for the errors is replaced by a weaker assumption of spherical symmetry. Structural distributions and confidence regions are derived, and it is shown that inference about means is identical with that appropriate under normality, being based on a matrix generalization of “Studentization”. Some relevant distribution theory is developed, the approach…

存在干扰参数时的充分性与辅助性概念AI 解读

Summary Examples are presented to show how ambiguities may arise from attempts to define and apply analogues of sufficiency and ancillarity in the presence of nuisance parameters. It is necessary to tread with caution if one wishes to avoid inconsistencies or unexpected consequences inherent in principles which, on first acquaintance, appear unexceptionable.

期望一致性与广义贝叶斯推断AI 解读

In a previous paper, the authors introduced a new criterion of expectation consistency between probability distributions of discrete data given discrete parameter values and arbitrary posterior probability distributions for the parameter. It is here shown, under very weak assumptions, that expectation consistency implies that the posterior distributions are generalized Bayes. However when the posterior distributions are generalized Bayes, the implied prior distribution need…

贝叶斯推断与结构推断中的边际化悖论AI 解读

Summary We describe a range of routine statistical problems in which marginal posterior distributions derived from improper prior measures are found to have an unBayesian property—one that could not occur if proper prior measures were employed. This paradoxical possibility is shown to have several facets that can be successfully analysed in the framework of a general group structure. The results cast a shadow on the uncritical use of improper prior measures. A separate…

大观测值下的后验期望AI 解读

For a single observation X = x from a distribution having unknown location parameter Θ we investigate the asymptotic behaviour of the posterior distribution of Θ, as x tends to infinity. Conditions are given for this posterior distribution to approach the prior distribution, and dual conditions under which the posterior distribution is ‘ asymptotically fiducial’. The former conditions apply when the prior distribution is normal and the error has a Student distribution, the…

常规统计问题中非正规先验贝叶斯推断的非贝叶斯后果AI 解读

For two routine statistical problems, inference about the ratio of two exponential means and inference about the coefficient of variation of a normal random variable, a serious pathology of Bayesian inference based on improper priors is uncovered and investigated.

常规统计问题中非正常先验贝叶斯推断的反贝叶斯后果AI 解读

For two routine statistical problems, inference about the ratio of two exponential means and inference about the coefficient of variation of a normal random variable, a serious pathology of Bayesian inference based on improper priors is uncovered and investigated.