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BUGS: Bayesian inference using Gibbs sampling, Version 0.6. Biostatistics Unit
, 1997
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Causal inference in statistics: An Overview
, 2009
"... This review presents empirical researcherswith recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all ca ..."
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Cited by 61 (12 self)
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This review presents empirical researcherswith recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects ” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret, ” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potentialoutcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.
On the Markov Equivalence of Chain Graphs, Undirected Graphs, and Acyclic Digraphs
 Scandinavian Journal of Statistics
, 1994
"... Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or fo ..."
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Cited by 39 (5 self)
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Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or for general chain graphs (which include both UDGs and ADGs as special cases). This paper addresses three questions regarding the equivalence of graphical Markov models: when is a given chain graph Markov equivalent (1) to some UDG? (2) to some (at least one) ADG? (3) to some decomposable UDG? The answers are obtained by means of an extension of Frydenberg's (1990) elegant graphtheoretic characterization of the Markov equivalence of chain graphs. 1 Introduction The use of graphs to represent dependence relations among random variables, first introduced by Wright (1921), has generated considerable research activity, especially since the early 1980s. Particular attention has been devoted to gra...
A SINful approach to Gaussian graphical model selection
 Journal of Statistical Planning and Inference
"... Abstract. Multivariate Gaussian graphical models are defined in terms of Markov properties, i.e., conditional independences associated with the underlying graph. Thus, model selection can be performed by testing these conditional independences, which are equivalent to specified zeroes among certain ..."
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Cited by 36 (5 self)
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Abstract. Multivariate Gaussian graphical models are defined in terms of Markov properties, i.e., conditional independences associated with the underlying graph. Thus, model selection can be performed by testing these conditional independences, which are equivalent to specified zeroes among certain (partial) correlation coefficients. For concentration graphs, covariance graphs, acyclic directed graphs, and chain graphs (both LWF and AMP), we apply Fisher’s ztransformation, ˇ Sidák’s correlation inequality, and Holm’s stepdown procedure, to simultaneously test the multiple hypotheses obtained from the Markov properties. This leads to a simple method for model selection that controls the overall error rate for incorrect edge inclusion. In practice, we advocate partitioning the simultaneous pvalues into three disjoint sets, a significant set S, an indeterminate set I, and a nonsignificant set N. Then our SIN model selection method selects two graphs, a graph whose edges correspond to the union of S and I, and a more conservative graph whose edges correspond to S only. Prior information about the presence and/or absence of particular edges can be incorporated readily. 1.
From association to causation via regression
 Indiana: University of Notre Dame
, 1997
"... For nearly a century, investigators in the social sciences have used regression models to deduce causeandeffect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend ..."
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Cited by 31 (7 self)
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For nearly a century, investigators in the social sciences have used regression models to deduce causeandeffect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work a principle honored more often in the breach than the observance.
Remarks concerning graphical models for time series and point processes
 Revista de Econometria
, 1996
"... Uma rede estatística é uma cole,cão de nós representando variáveis aleatórias e um conjunto de arestas que ligam os nós. Um modelo estocástico por isso e chamado um modelo gráfico. Estes modelos, de gráficos e redes, sáo particularmente úteis para examinar as dependéncias estatísticas baseadas em co ..."
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Cited by 31 (3 self)
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Uma rede estatística é uma cole,cão de nós representando variáveis aleatórias e um conjunto de arestas que ligam os nós. Um modelo estocástico por isso e chamado um modelo gráfico. Estes modelos, de gráficos e redes, sáo particularmente úteis para examinar as dependéncias estatísticas baseadas em condi,coes do tipo das que ocorrem frequentemente em economia e estatística. Neste artigo as variáveis aleatórias dos nós serão séries temporais ou processos pontuais. Os casos de gráfos direcionados e nãodirecionados são apresentados. A statistical network is a collection of nodes representing random variables and a set of edges that connect the nodes. A probabilistic model for such is called a graphical model. These models, graphs and networks are particularly useful for examining statistical dependencies based on conditioning as often occurs in economics and statistics. In this paper the nodal random variables will be time series or point proceses. The cases of undirected and directed graphs are focussed on.
Multiple testing and error control in Gaussian graphical model selection
 Statistical Science
"... Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of cond ..."
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Cited by 30 (4 self)
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Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of conditional independences that is imposed on the variables ’ joint distribution. Focusing on Gaussian models, we review classical graphical models. For these models the defining conditional independences are equivalent to vanishing of certain (partial) correlation coefficients associated with individual edges that are absent from the graph. Hence, Gaussian graphical model selection can be performed by multiple testing of hypotheses about vanishing (partial) correlation coefficients. We show and exemplify how this approach allows one to perform model selection while controlling error rates for incorrect edge inclusion. Key words and phrases: Acyclic directed graph, Bayesian network, bidirected graph, chain graph, concentration graph, covariance graph, DAG, graphical model, multiple testing, undirected graph. 1.
Bayesian inference for nondecomposable graphical Gaussian models
 Sankhya, Ser. A
, 2003
"... In this paper we propose a method to calculate the posterior probability of a nondecomposable graphical Gaussian model. Our proposal is based on a new device to sample from Wishart distributions, conditional on the graphical constraints. As a result, our methodology allows Bayesian model selection w ..."
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Cited by 19 (0 self)
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In this paper we propose a method to calculate the posterior probability of a nondecomposable graphical Gaussian model. Our proposal is based on a new device to sample from Wishart distributions, conditional on the graphical constraints. As a result, our methodology allows Bayesian model selection within the whole class of graphical Gaussian models, including nondecomposable ones. 1 INTRODUCTION Let G be a conditional independence graph, describing the association structure of a vector of random variables, say X. A graphical model is a family of probability distributions P G which is Markov over G. In particular, when all the random variables in X are continuous, a graphical Gaussian model is obtained by assuming P G = N(¯; \Sigma G ), with \Sigma G positive definite and such that P G is Markov over G. For an introduction to graphical models, see for instance Lauritzen (1996) or Whittaker (1990). Typically the association structure of X is uncertain and, thus, has to be inferred from...