## Causal Inference from Graphical Models (2001)

Citations: | 65 - 5 self |

### BibTeX

@MISC{Lauritzen01causalinference,

author = {Steffen L Lauritzen},

title = {Causal Inference from Graphical Models},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particular those based upon directed acyclic graphs, have natural causal interpretations and thus form a base for a language in which causal concepts can be discussed and analysed in precise terms. As a consequence there has been an explosion of writings, not primarily within mainstream statistical literature, concerned with the exploitation of this language to clarify and extend causal concepts. Among these we mention in particular books by Spirtes, Glymour and Scheines (1993), Shafer (1996), and Pearl (2000) as well as the collection of papers in Glymour and Cooper (1999). Very briefly, but fundamentally,

### Citations

1457 |
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Citation Context ...tial role in this justification process. A particular modelling formulation, leading to causal Markov models, has documented its relevance in several areas of application. Structural equation models (=-=Bollen 1989-=-) were invented in the context of genetics (Wright 1921, 1923, 1934), and exploited in economics (Haavelmo 1943; Wold 1954) and social sciences (Goldberger 1972), see for example Pearl (1998) and Spir... |

1371 |
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Citation Context ... instrumental variables, partial compliance, potential responses, structural equations. 1 Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (=-=Lauritzen and Spiegelhalter 1988-=-; Shenoy and Shafer 1990; Jensen et al. 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graph... |

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1189 |
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Citation Context ...ing subgraph is displayed as the left graph in Fig. 4. This is again to be contrasted with the effect of observation of variable 5, which creates a dependence structure determined by the chain graph (=-=Lauritzen 1996-=-) to the right in the same figure. This is due to the factor p(x 5 j x 2 ; x 3 ) creating a function depending on (x 2 ; x 3 ) in the factorization (15). It is important to realize that successive con... |

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(Show Context)
Citation Context ... variable. Note the similarity with the situation of partial compliance described in Figure 9, where the assignment variable a is an instrument. important in econometrics (Bowden and Turkington 1984; =-=Angrist et al. 1996-=-). An instrumental variable is one which affects the treatment, but is uncorrelated with unobserved factors. An instrumental variable can be used to derive bounds for treatment effects as we shall sho... |

548 |
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(Show Context)
Citation Context ...t of sometimes quite heated discussions (Freedman 1991, 1995; Robins and Wasserman 1999; Glymourset al. 1999). Basically there have been two different types of approach. The constraintbased approach (=-=Spirtes et al. 1993-=-) is generally conceived to take place in an ideal environment where the joint distribution P of a system X of random variables is known completely without error, whereas the causal graph D which has ... |

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Citation Context ...(randomized) decision policies, but here we only consider the simpler case. This approach to the representation of causal effects is related to so-called influence diagrams (Howard and Matheson 1984; =-=Shachter 1986-=-; Smith 1989; Oliver and Smith 1990) and taking this connection to its consequence gives yet an alternative basis for causal interpretation of graphical models (Heckerman and Shachter 1995). Each of t... |

405 | Fusion, propagation and structuring in belief networks
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Citation Context ..., identification of treatment effects, influence diagrams, instrumental variables, partial compliance, potential responses, structural equations. 1 Introduction The introduction of Bayesian networks (=-=Pearl 1986-=-b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988; Shenoy and Shafer 1990; Jensen et al. 1990) has initiated a renewed interest for understanding causal concepts in conn... |

380 |
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Citation Context ...ff vary in the set of all (randomized) decision policies, but here we only consider the simpler case. This approach to the representation of causal effects is related to so-called influence diagrams (=-=Howard and Matheson 1984-=-; Shachter 1986; Smith 1989; Oliver and Smith 1990) and taking this connection to its consequence gives yet an alternative basis for causal interpretation of graphical models (Heckerman and Shachter 1... |

369 |
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Citation Context ...le in the methods developed by Robins (1996, 1997), although it is usually introduced in a slightly different context. Counterfactual objects have at all times been at the basis for causal reasoning (=-=Lewis 1973-=-). Note that in the formulation given above, the variables\Omega v are no more and no less counterfactual than the ! used when a random variable X is considered to be a deterministic function X(!) of ... |

295 |
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(Show Context)
Citation Context ...ponses, structural equations. 1 Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988; Shenoy and Shafer 1990; =-=Jensen et al. 1990-=-) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particular those based upon ... |

225 | Bayesian Inference for Causal Effects: The Role of Randomization,” The - Rubin - 1978 |

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(Show Context)
Citation Context ...odelling formulation, leading to causal Markov models, has documented its relevance in several areas of application. Structural equation models (Bollen 1989) were invented in the context of genetics (=-=Wright 1921-=-, 1923, 1934), and exploited in economics (Haavelmo 1943; Wold 1954) and social sciences (Goldberger 1972), see for example Pearl (1998) and Spirtes et al. (1998) for further discussion. They were use... |

149 | Independence properties of directed markov fields - Lauritzen, Dawid, et al. - 1990 |

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125 |
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(Show Context)
Citation Context ... has documented its relevance in several areas of application. Structural equation models (Bollen 1989) were invented in the context of genetics (Wright 1921, 1923, 1934), and exploited in economics (=-=Haavelmo 1943-=-; Wold 1954) and social sciences (Goldberger 1972), see for example Pearl (1998) and Spirtes et al. (1998) for further discussion. They were used as the main justification and motivation for studying ... |

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(Show Context)
Citation Context ...eneral criterion for deciding when two groups of variables A and B are conditionally independent given a third group of variables S. Moreover, it cannot be further strengthened. For example it holds (=-=Frydenberg 1990-=-b) that if all state spaces are binary, i.e. X ff = f1; \Gamma1g, then A??B j S for all P 2 M F (G) () S separates A from B: In other words, if A and B are not separated by S then there is a factorizi... |

109 | Causal inference without counterfactuals (with discussion - Dawid - 2000 |

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95 | The Analysis of Randomized and Non-Randomized AIDS Treatment Trials Using A New Approach To Causal Inference - Robins - 1989 |

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78 | Causal inference from complex longitudinal data - Robins - 1997 |

77 |
Instrumental Variables
- Bowden, Turkington
- 1984
(Show Context)
Citation Context ...ng that i is an instrumental variable. Note the similarity with the situation of partial compliance described in Figure 9, where the assignment variable a is an instrument. important in econometrics (=-=Bowden and Turkington 1984-=-; Angrist et al. 1996). An instrumental variable is one which affects the treatment, but is uncorrelated with unobserved factors. An instrumental variable can be used to derive bounds for treatment ef... |

77 | Discovering Causal Structure - Glymour, Scheines, et al. - 1987 |

75 |
Probabilistic Inference in Intelligent Systems: Networks of Plausible Inference
- Pearl
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(Show Context)
Citation Context ...s formal axioms for conditional independence or irrelevance. A semi-graphoid is an algebraic structure which satisfies (C1')--(C4'). If also (C5') holds for disjoint subsets, it is called a graphoid (=-=Pearl 1988-=-). Similarly we refer to (C1')--(C4') as the semi-graphoid axioms and (C1')--(C5') as the graphoid axioms. 4 Markov properties for undirected graphs Conditional independence properties of joint distri... |

75 |
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(Show Context)
Citation Context ...resents the way in which a probability distribution, P (Y = y), should be modified when the information X = x is revealed. Paradoxes appear when it is unclear how the information about X is revealed (=-=Shafer 1985-=-, 1996), but that is a different discussion. When discussing causal issues it is important to realize that this is typically not the way the distribution of Y should be modified if we intervene extern... |

64 |
G.: Axioms for probability and belief function propagation
- Shenoy, Shafer
- 1990
(Show Context)
Citation Context ...ompliance, potential responses, structural equations. 1 Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988; =-=Shenoy and Shafer 1990-=-; Jensen et al. 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particul... |

61 | Recursive causal models - Kiiveri, Speed, et al. - 1984 |

60 | Bayesian inference for causal effects in randomized experiments with noncompliance - IMBENS, RUBIN - 1997 |

56 |
Influence Diagrams, Belief Nets and Decision Analysis
- Oliver, Smith
- 1990
(Show Context)
Citation Context ...ies, but here we only consider the simpler case. This approach to the representation of causal effects is related to so-called influence diagrams (Howard and Matheson 1984; Shachter 1986; Smith 1989; =-=Oliver and Smith 1990-=-) and taking this connection to its consequence gives yet an alternative basis for causal interpretation of graphical models (Heckerman and Shachter 1995). Each of the variables F ff ; ff 2 A, where A... |

54 | Decisiontheoretic foundations for causal reasoning
- Heckerman, Shachter
- 1995
(Show Context)
Citation Context ...Howard and Matheson 1984; Shachter 1986; Smith 1989; Oliver and Smith 1990) and taking this connection to its consequence gives yet an alternative basis for causal interpretation of graphical models (=-=Heckerman and Shachter 1995-=-). Each of the variables F ff ; ff 2 A, where A is the set of variables for which intervention is contemplated, can be given an arbitrary distribution with positive probability of all states. We then ... |

53 | Graphs, causality, and structural equation models - Pearl - 1998 |

50 | Compliance as an Explanatory Variable in Clinical Trials” (with discussion - Efron, Feldman - 1991 |

46 | Computation, causation, and discovery - Glymour, Cooper - 1999 |

44 | Strong completeness and faithfulness in Bayesian networks - Meek - 1995 |

44 | Directed cyclic graphical representations of feedback models - Spirtes - 1995 |