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Aspects Of Graphical Models Connected With Causality
, 1993
"... This paper demonstrates the use of graphs as a mathematical tool for expressing independenices, and as a formal language for communicating and processing causal information in statistical analysis. We show how complex information about external interventions can be organized and represented graphica ..."
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Cited by 13 (10 self)
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This paper demonstrates the use of graphs as a mathematical tool for expressing independenices, and as a formal language for communicating and processing causal information in statistical analysis. We show how complex information about external interventions can be organized and represented graphically and, conversely, how the graphical representation can be used to facilitate quantitative predictions of the effects of interventions. We first review the Markovian account of causation and show that directed acyclic graphs (DAGs) offer an economical scheme for representing conditional independence assumptions and for deducing and displaying all the logical consequences of such assumptions. We then introduce the manipulative account of causation and show that any DAG defines a simple transformation which tells us how the probability distribution will change as a result of external interventions in the system. Using this transformation it is possible to quantify, from nonexperimental data...
A Queue with Periodic Arrivals and Constant Service Rate
 In Chapter 10 of Probability, Statistics and Optimization a Tribute
, 1994
"... : Consider a queueing system in which K sources each generate 1=M units of work once every time unit. The phases of the sources are mutually independent, and each phase is uniformly distributed over the unit interval. The queue is served at unit rate. The distribution of the typical work and the max ..."
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Cited by 8 (1 self)
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: Consider a queueing system in which K sources each generate 1=M units of work once every time unit. The phases of the sources are mutually independent, and each phase is uniformly distributed over the unit interval. The queue is served at unit rate. The distribution of the typical work and the maximum work are studied both for finite K and M and in the limit of large K and M . The limiting maximum work is identified as the maximum of a reflecting Brownian motion over the unit interval given that its local time at zero first reaches a specified value at the end of the interval. The analysis is expedited by a tie to the empirical process arising in KolmogorovSmirnov statistical tests. 1
SHARP PROBABILITY ESTIMATES FOR GENERALIZED SMIRNOV STATISTICS
"... Dedicated to the memory of Walter Philipp Abstract. We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform[0, 1] random variables stays to one side of a given line. 1. ..."
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Cited by 6 (2 self)
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Dedicated to the memory of Walter Philipp Abstract. We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform[0, 1] random variables stays to one side of a given line. 1.
Logicist Statistics I. Models and Modeling
 Statistical Science
, 1998
"... Abstract. Arguments are presented to support increased emphasis on logical aspects of formal methods of analysis, depending on probability in the sense of R. A. Fisher. Formulating probabilistic models that convey uncertain knowledge of objective phenomena and using such models for inductive reasoni ..."
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Cited by 5 (0 self)
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Abstract. Arguments are presented to support increased emphasis on logical aspects of formal methods of analysis, depending on probability in the sense of R. A. Fisher. Formulating probabilistic models that convey uncertain knowledge of objective phenomena and using such models for inductive reasoning are central activities of individuals that introduce limited but necessary subjectivity into science. Statistical models are classified into overlapping types called here empirical, stochastic and predictive, all drawing on a common mathematical theory of probability, and all facilitating statements with logical and epistemic content. Contexts in which these ideas are intended to apply are discussed via three major examples. Key words and phrases: Logicism and proceduralism; specificity of analysis; formal subjective probability; complementarity; subjective and objective; formal and informal; empirical, stochastic and predictive models; U.S. national census; screening for chronic disease; global climate change.
Teaching Causal Inference In Experiments and Observational Studies
 ASA 1999
, 1999
"... Inference for causal effects is a critical activity in many branches of science and public policy. The field of statistics is the one field most suited to address such problems, whether from designed experiments or observational studies. Consequently, it is arguably essential that departments of sta ..."
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Inference for causal effects is a critical activity in many branches of science and public policy. The field of statistics is the one field most suited to address such problems, whether from designed experiments or observational studies. Consequently, it is arguably essential that departments of statistics teach courses in causal inference to both graduate and undergraduate students. This presentation will discuss some aspects of such courses based on: a graduate level course taught at Harvard for a half dozen years, sometimes jointly with the Department of Economics (with Professor Guido Imbens, now at UCLA), and current plans for an undergraduate core course at Harvard University. An expanded version of this brief document will outline the courses ' contents more completely. Moreover, a textbook by Imbens and Rubin, due to appear in 2000, will cover the basic material needed in both courses. The current course at Harvard begins with the definition of causal effects through potential outcomes. Causal estimands are comparisons of the outcomes that would have been observed under different exposures of units to treatments. This approach is commonly referred to as 'Rubin's Causal Model RCM " (Holland, 1986), but the formal notation in the context of randomizationbased inference in randomized experiments goes back to Neyman (1923), and the intuitive idea goes back centuries in various literatures; see also Fisher (1918), Tinbergen (1930) and Haavelmo (1944). The label "RCM " arises because of extensions (e.g., Rubin, 1974, 1977, 1978) that