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Russian roulette: the need for stochastic potential outcomes when utilities depend on counterfactuals

俄罗斯轮盘赌:效用依赖反事实时为何需要随机潜在结果

Summary It has been proposed in medical decision analysis to express the ‘first, do no harm’ principle as an asymmetric utility function in which the loss from killing a patient would count more than the gain from saving a life. Such a utility depends on unrealized potential outcomes, and we show how this yields a paradoxical decision recommendation in a simple hypothetical example involving games of Russian roulette. The problem is resolved if we abandon the stable unit…

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What is a standard error?

什么是标准误?

In statistics, the standard error has a clear technical definition: it is the estimated standard deviation of a parameter estimate. In practice, though, challenges arise when we go beyond the simple balls-in-urn model to consider generalizations beyond the population from which the data were sampled. This is important because generalization is nearly always the goal of quantitative studies. In this brief paper we consider three examples.

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Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs

为何不应在断点回归设计中使用高阶多项式

It is common in regression discontinuity analysis to control for third, fourth, or higher-degree polynomials of the forcing variable. There appears to be a perception that such methods are theoretically justified, even though they can lead to evidently nonsensical results. We argue that controlling for global high-order polynomials in regression discontinuity analysis is a flawed approach with three major problems: it leads to noisy estimates, sensitivity to the degree of…

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Estimating Incumbency Advantage and Its Variation, as an Example of a Before–After Study

任职优势及其差异的估计:一项前后比较研究

Incumbency advantage is one of the most widely studied features in American legislative elections. In this article we construct and implement an estimate that allows incumbency advantage to vary between individual incumbents. This model predicts that open-seat elections will be less variable than those with incumbents running, an observed empirical pattern that is not explained by previous models. We apply our method to the U.S. House of Representatives in the twentieth…

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How Many People Do You Know in Prison?

你认识多少在监狱中的人?

Networks—sets of objects connected by relationships—are important in a number of fields. The study of networks has long been central to sociology, where researchers have attempted to understand the causes and consequences of the structure of relationships in large groups of people. Using insight from previous network research, Killworth et al. and McCarty et al. have developed and evaluated a method for estimating the sizes of hard-to-count populations using network data…

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Regression Modeling and Meta-Analysis for Decision Making

用于决策的回归建模与元分析

Regression models are often used, explicitly or implicitly, for decision making. However, the choices made in setting up the models (e.g., inclusion of predictors based on statistical significance) do not map directly into decision procedures. Bayesian inference works more naturally with decision analysis but presents problems in practice when noninformative prior distributions are used with sparse data. We do not attempt to provide a general solution to this problem, but…

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Poststratification Without Population Level Information on the Poststratifying Variable With Application to Political Polling

缺少总体分层变量信息时的后分层:政治民调应用

We investigate the construction of more precise estimates of a collection of population means using information about a related variable in the context of repeated sample surveys. The method is illustrated using poll results concerning presidential approval rating (our related variable is political party identification). We use poststratification to construct these improved estimates, but because we do not have population level information on the poststratifying variable, we…

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Not Asked and Not Answered: Multiple Imputation for Multiple Surveys

未提问与未回答:多项调查的多重插补

We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked or different sampling methods are used in different strata or clusters. Our method involves multiply imputing the missing items and questions by adding to existing methods of imputation…

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Not Asked and Not Answered: Multiple Imputation for Multiple Surveys

未问与未答:多项调查的多重插补

We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked or different sampling methods are used in different strata or clusters. Our method involves multiply imputing the missing items and questions by adding to existing methods of imputation…

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Estimating the Probability of Events That have Never Occurred: When is Your Vote Decisive?

估计从未发生事件的概率:你的一票何时具有决定性?

Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that…

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Estimating the Probability of Events That Have Never Occurred: When Is Your Vote Decisive?

估计从未发生事件的概率:你的一票何时具有决定性?

Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that…

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Characterizing a Joint Probability Distribution by Conditionals

利用条件分布刻画联合概率分布

SUMMARY We derive conditions under which a set of conditional and marginal probability distributions will uniquely specify an all-positive joint distribution. Our theoretical result may yield insights into the construction and simulation of multivariate probability models.

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Estimating the Electoral Consequences of Legislative Redistricting

估计立法选区重划的选举后果

We analyze the effects of redistricting as revealed in the votes received by the Democratic and Republican candidates for state legislature. We develop measures of partisan bias and the responsiveness of the composition of the legislature to changes in statewide votes. Our statistical model incorporates a mixed hierarchical Bayesian and non-Bayesian estimation, requiring simulation along the lines of Tanner and Wong (1987). This model provides reliable estimates of partisan…

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Estimating the Electoral Consequences of Legislative Redistricting

估计立法选区重划的选举后果

We analyze the effects of redistricting as revealed in the votes received by the Democratic and Republican candidates for state legislature. We develop measures of partisan bias and the responsiveness of the composition of the legislature to changes in statewide votes. Our statistical model incorporates a mixed hierarchical Bayesian and non-Bayesian estimation, requiring simulation along the lines of Tanner and Wong (1987). This model provides reliable estimates of partisan…

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