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Table of Contents
Intro
Probabilistic and Causal Inference: The Works of Judea Pearl
Contents
Preface
Credits
I INTRODUCTION
1 Biography of Judea Pearl by Stuart J. Russell
References
2 Turing Award Lecture
References
3 Interview by Martin Ford
References
4 An Interview with Ron Wassertein on How The Book of Why Transforms Statistics
5 Selected Annotated Bibliography by Judea Pearl
Search and Heuristics
Bayesian Networks
Causality
Causal, Casual, and Curious
II HEURISTICS
6 Introduction by Judea Pearl
References
7 Asymptotic Properties of Minimax Trees and Game-Searching Procedures
Abstract
7.1 The Probability of Winning a Standard h-level Game Tree with Random WIN Positions
7.2 Game Trees with an Arbitrary Distribution of Terminal Values
7.3 The Mean Complexity of Solving (h, d, P0)-game
7.4 Solving, Testing, and Evaluating Game Trees
7.5 Test and, if Necessary, Evaluate-The SCOUT Algorithm
7.6 Analysis of SCOUT's Expected Performance
7.7 On the Branching Factor of the ALPHA-BETA (α-β) procedure
References
8 The Solution for the Branching Factor of the Alpha-Beta Pruning Algorithm and its Optimality
8.1 Introduction
8.1.1 Informal Description of the α-β Procedure
8.1.2 Previous Analytical Results
8.2 Analysis
8.2.1 An Integral Formula for Nn,d
8.2.2 Evaluation of Rα-β
8.3 Conclusions
References
9 On the Discovery and Generation of Certain Heuristics
Abstract
9.1 Introduction: Typical Uses of Heuristics
9.1.1 The Traveling Salesman Problem (TSP)
9.1.2 Some Properties of Heuristics
9.1.3 Where do these Heuristics Come from?
9.2 Mechanical Generation of Admissible Heuristics
9.3 Can a Program Tell an Easy Problem When It Sees One?
9.4 Conclusions
9.4.1 Bibliographical and Historical Remarks
References.
III PROBABILITIES
10 Introduction by Judea Pearl
References
11 Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach
Abstract
11.1 Introduction
11.2 Definitions and Nomenclature
11.3 Structural Assumptions
11.4 Combining Top and Bottom Evidences
11.5 Propagation of Information Through the Network
11.6 A Token Game Illustration
11.7 Properties of the Updating Scheme
11.8 A Summary of Proofs
11.9 Conclusions
References
12 Fusion, Propagation, and Structuring in Belief Networks
Abstract
12.1 Introduction
12.1.1 Belief Networks
12.1.2 Conditional Independence and Graph Separability
12.1.3 An Outline and Summary of Results
12.2 Fusion and Propagation
12.2.1 Autonomous Propagation as a Computational Paradigm
12.2.2 Belief Propagation in Trees
12.2.2.1 Data Fusion
12.2.2.2 Propagation Mechanism
12.2.2.3 Illustrating the Flow of Belief
12.2.2.4 Properties of the Updating Scheme
12.2.3 Propagation in Singly Connected Networks
12.2.3.1 Fusion Equations
12.2.3.2 Propagation Equation
12.2.4 Summary and Extensions for Multiply Connected Networks
12.3 Structuring Causal Trees
12.3.1 Causality, Conditional Independence, and Tree Architecture
12.3.2 Problem Definition and Nomenclature
12.3.3 Star-Decomposable Triplets
12.3.4 A Tree-Reconstruction Procedure
12.3.5 Conclusions and Open Questions
12.A Appendix A. Derivation of the Updating Rules for Singly Connected Networks
12.A.1 Updating BEL
12.A.2 Updating π
12.A.3 Updating λ
12.B Appendix B. Conditions for Star-decomposability
Acknowledgments
References
13 GRAPHOIDS: Graph-Based Logic for Reasoning about Relevance Relations Or When Would x Tell You More about y If You Already Know z?
Abstract
13.1 Introduction.
13.2 Probabilistic Dependencies and their Graphical Representation
13.3 GRAPHOIDS
13.4 Special Graphoids and Open Problems
13.4.1 Graph-induced Graphoids
13.4.2 Probabilistic Graphoids
13.4.3 Correlational Graphoids
13.5 Conclusions
References
14 System Z: A Natural Ordering of Defaults with Tractable Applications to Nonmonotonic Reasoning
Abstract
14.1 Description
14.2 Consequence Relations
14.3 Illustrations
14.4 The Maximum Entropy Approach
14.5 Conditional Entailment
14.6 Conclusions
Acknowledgments
14.I Appendix I: Uniqueness of The Minimal Ranking Function
14.II Appendix II: Rational Monotony of Admissible Rankings
References
IV CAUSALITY 1988-2001
15 Introduction by Judea Pearl
References
16 Equivalence and Synthesis of Causal Models
Abstract
16.1 Introduction
16.2 Patterns of Causal Models
16.3 Embedded Causal Models
16.4 Applications to the Synthesis of Causal Models
IC-Algorithm (Inductive Causation)
Acknowledgments
References
17 Probabilistic Evaluation of Counterfactual Queries
Abstract
17.1 Introduction
17.2 Notation
17.3 Party Example
17.4 Probabilistic vs. Functional Specification
17.5 Evaluating Counterfactual Queries
17.6 Party Again
17.7 Special Case: Linear-Normal Models
17.8 Conclusion
Acknowledgments
References
18 Causal Diagrams for Empirical Research (With Discussions)
Summary
Some key words
18.1 Introduction
18.2 Graphical Models and the Manipulative Account of Causation
18.2.1 Graphs and Conditional Independence
18.2.2 Graphs as Models of Interventions
18.3 Controlling Confounding Bias
18.3.1 The Back-Door Criterion
18.3.2 The Front-Door Criteria
18.4 A Calculus of Intervention
18.4.1 General
18.4.2 Preliminary Notation
18.4.3 Inference Rules.
18.4.4 Symbolic Derivation of Causal Effects: An Example
18.4.5 Causal Inference by Surrogate Experiments
18.5 Graphical Tests of Identifiability
18.5.1 General
18.5.2 Identifying Models
18.5.3 Nonidentifying Models
18.6 Discussion
Acknowledgments
18.A Appendix
Proof of Theorem 18.3
References
18.I Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.II Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.III Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.IV Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.V Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.VI Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.VI.A Introduction
18.VI.B Task 1
18.VI.B.1 General
18.VI.B.2 A Causal Model
18.VI.B.3 Relationship with Pearl's Work
18.VI.C Task 2
18.VII Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.VII.A Successful and Unsuccessful Causal Inference: Some Examples
18.VII.B Warranted Inferences
18.VIII Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.IX Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.IX.A Introduction
18.IX.B Ignorability and the Back-Door Criterion
18.X Rejoinder to Discussions of 'Causal Diagrams for Empirical Research'
18.X.A General
18.X.B Graphs, Structural Equations and Counterfactuals
18.X.C The Equivalence of Counterfactual and Structural Analyses
18.X.D Practical Versus Hypothetical Interventions
18.X.E Intervention as Conditionalisation
18.X.F Testing Versus using Assumptions
18.X.G Causation Versus Dependence
18.X.H Exemplifying Modelling Errors
18.X.I The Myth of Dangerous Graphs
Additional References.
19 Probabilities of Causation: Three Counterfactual Interpretations and Their Identification
Abstract
19.1 Introduction
19.2 Structural Model Semantics (A Review)
19.2.1 Definitions: Causal Models, Actions and Counterfactuals
19.2.2 Examples
19.2.3 Relation to Lewis' Counterfactuals
19.2.4 Relation to Probabilistic Causality
19.2.5 Relation to Neyman-Rubin Model
19.3 Necessary and Sufficient Causes: Conditions of Identification
19.3.1 Definitions, Notations, and Basic Relationships
19.3.2 Bounds and Basic Relationships under Exogeneity
19.3.3 Identifiability under Monotonicity and Exogeneity
19.3.4 Identifiability under Monotonicity and Non-Exogeneity
19.4 Examples and Applications
19.4.1 Example 1: Betting against a Fair Coin
19.4.2 Example 2: The Firing Squad
19.4.3 Example 3: The Effect of Radiation on Leukemia
19.4.4 Example 4: Legal Responsibility from Experimental and Nonexperimental Data
19.5 Identification in Non-Monotonic Models
19.6 From Necessity and Sufficiency to "Actual Cause"
19.6.1 The Role of Structural Information
19.6.2 Singular Sufficient Causes
19.6.3 Example: The Desert Traveler (after P. Suppes)
19.6.3.1 Necessity and Sufficiency Ignoring Internal Structure
19.6.3.2 Sufficiency and Necessity given Forensic Reports
19.6.3.3 Necessity Given Forensic Reports
19.7 Conclusion
19.A Appendix: The Empirical Content of Counterfactuals
References
20 Direct and Indirect Effects
Abstract
20.1 Introduction
20.2 Conceptual Analysis
20.2.1 Direct versus Total Effects
20.2.2 Descriptive versus Prescriptive Interpretation
20.2.3 Policy Implications of the Descriptive Interpretation
20.2.4 Descriptive Interpretation of Indirect Effects
20.3 Formal Analysis
20.3.1 Notation
20.3.2 Controlled Direct Effects (review).
20.3.3 Natural Direct Effects: Formulation.
Probabilistic and Causal Inference: The Works of Judea Pearl
Contents
Preface
Credits
I INTRODUCTION
1 Biography of Judea Pearl by Stuart J. Russell
References
2 Turing Award Lecture
References
3 Interview by Martin Ford
References
4 An Interview with Ron Wassertein on How The Book of Why Transforms Statistics
5 Selected Annotated Bibliography by Judea Pearl
Search and Heuristics
Bayesian Networks
Causality
Causal, Casual, and Curious
II HEURISTICS
6 Introduction by Judea Pearl
References
7 Asymptotic Properties of Minimax Trees and Game-Searching Procedures
Abstract
7.1 The Probability of Winning a Standard h-level Game Tree with Random WIN Positions
7.2 Game Trees with an Arbitrary Distribution of Terminal Values
7.3 The Mean Complexity of Solving (h, d, P0)-game
7.4 Solving, Testing, and Evaluating Game Trees
7.5 Test and, if Necessary, Evaluate-The SCOUT Algorithm
7.6 Analysis of SCOUT's Expected Performance
7.7 On the Branching Factor of the ALPHA-BETA (α-β) procedure
References
8 The Solution for the Branching Factor of the Alpha-Beta Pruning Algorithm and its Optimality
8.1 Introduction
8.1.1 Informal Description of the α-β Procedure
8.1.2 Previous Analytical Results
8.2 Analysis
8.2.1 An Integral Formula for Nn,d
8.2.2 Evaluation of Rα-β
8.3 Conclusions
References
9 On the Discovery and Generation of Certain Heuristics
Abstract
9.1 Introduction: Typical Uses of Heuristics
9.1.1 The Traveling Salesman Problem (TSP)
9.1.2 Some Properties of Heuristics
9.1.3 Where do these Heuristics Come from?
9.2 Mechanical Generation of Admissible Heuristics
9.3 Can a Program Tell an Easy Problem When It Sees One?
9.4 Conclusions
9.4.1 Bibliographical and Historical Remarks
References.
III PROBABILITIES
10 Introduction by Judea Pearl
References
11 Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach
Abstract
11.1 Introduction
11.2 Definitions and Nomenclature
11.3 Structural Assumptions
11.4 Combining Top and Bottom Evidences
11.5 Propagation of Information Through the Network
11.6 A Token Game Illustration
11.7 Properties of the Updating Scheme
11.8 A Summary of Proofs
11.9 Conclusions
References
12 Fusion, Propagation, and Structuring in Belief Networks
Abstract
12.1 Introduction
12.1.1 Belief Networks
12.1.2 Conditional Independence and Graph Separability
12.1.3 An Outline and Summary of Results
12.2 Fusion and Propagation
12.2.1 Autonomous Propagation as a Computational Paradigm
12.2.2 Belief Propagation in Trees
12.2.2.1 Data Fusion
12.2.2.2 Propagation Mechanism
12.2.2.3 Illustrating the Flow of Belief
12.2.2.4 Properties of the Updating Scheme
12.2.3 Propagation in Singly Connected Networks
12.2.3.1 Fusion Equations
12.2.3.2 Propagation Equation
12.2.4 Summary and Extensions for Multiply Connected Networks
12.3 Structuring Causal Trees
12.3.1 Causality, Conditional Independence, and Tree Architecture
12.3.2 Problem Definition and Nomenclature
12.3.3 Star-Decomposable Triplets
12.3.4 A Tree-Reconstruction Procedure
12.3.5 Conclusions and Open Questions
12.A Appendix A. Derivation of the Updating Rules for Singly Connected Networks
12.A.1 Updating BEL
12.A.2 Updating π
12.A.3 Updating λ
12.B Appendix B. Conditions for Star-decomposability
Acknowledgments
References
13 GRAPHOIDS: Graph-Based Logic for Reasoning about Relevance Relations Or When Would x Tell You More about y If You Already Know z?
Abstract
13.1 Introduction.
13.2 Probabilistic Dependencies and their Graphical Representation
13.3 GRAPHOIDS
13.4 Special Graphoids and Open Problems
13.4.1 Graph-induced Graphoids
13.4.2 Probabilistic Graphoids
13.4.3 Correlational Graphoids
13.5 Conclusions
References
14 System Z: A Natural Ordering of Defaults with Tractable Applications to Nonmonotonic Reasoning
Abstract
14.1 Description
14.2 Consequence Relations
14.3 Illustrations
14.4 The Maximum Entropy Approach
14.5 Conditional Entailment
14.6 Conclusions
Acknowledgments
14.I Appendix I: Uniqueness of The Minimal Ranking Function
14.II Appendix II: Rational Monotony of Admissible Rankings
References
IV CAUSALITY 1988-2001
15 Introduction by Judea Pearl
References
16 Equivalence and Synthesis of Causal Models
Abstract
16.1 Introduction
16.2 Patterns of Causal Models
16.3 Embedded Causal Models
16.4 Applications to the Synthesis of Causal Models
IC-Algorithm (Inductive Causation)
Acknowledgments
References
17 Probabilistic Evaluation of Counterfactual Queries
Abstract
17.1 Introduction
17.2 Notation
17.3 Party Example
17.4 Probabilistic vs. Functional Specification
17.5 Evaluating Counterfactual Queries
17.6 Party Again
17.7 Special Case: Linear-Normal Models
17.8 Conclusion
Acknowledgments
References
18 Causal Diagrams for Empirical Research (With Discussions)
Summary
Some key words
18.1 Introduction
18.2 Graphical Models and the Manipulative Account of Causation
18.2.1 Graphs and Conditional Independence
18.2.2 Graphs as Models of Interventions
18.3 Controlling Confounding Bias
18.3.1 The Back-Door Criterion
18.3.2 The Front-Door Criteria
18.4 A Calculus of Intervention
18.4.1 General
18.4.2 Preliminary Notation
18.4.3 Inference Rules.
18.4.4 Symbolic Derivation of Causal Effects: An Example
18.4.5 Causal Inference by Surrogate Experiments
18.5 Graphical Tests of Identifiability
18.5.1 General
18.5.2 Identifying Models
18.5.3 Nonidentifying Models
18.6 Discussion
Acknowledgments
18.A Appendix
Proof of Theorem 18.3
References
18.I Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.II Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.III Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.IV Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.V Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.VI Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.VI.A Introduction
18.VI.B Task 1
18.VI.B.1 General
18.VI.B.2 A Causal Model
18.VI.B.3 Relationship with Pearl's Work
18.VI.C Task 2
18.VII Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.VII.A Successful and Unsuccessful Causal Inference: Some Examples
18.VII.B Warranted Inferences
18.VIII Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.IX Discussion of 'Causal Diagrams for Empirical Research' by J. Pearl
18.IX.A Introduction
18.IX.B Ignorability and the Back-Door Criterion
18.X Rejoinder to Discussions of 'Causal Diagrams for Empirical Research'
18.X.A General
18.X.B Graphs, Structural Equations and Counterfactuals
18.X.C The Equivalence of Counterfactual and Structural Analyses
18.X.D Practical Versus Hypothetical Interventions
18.X.E Intervention as Conditionalisation
18.X.F Testing Versus using Assumptions
18.X.G Causation Versus Dependence
18.X.H Exemplifying Modelling Errors
18.X.I The Myth of Dangerous Graphs
Additional References.
19 Probabilities of Causation: Three Counterfactual Interpretations and Their Identification
Abstract
19.1 Introduction
19.2 Structural Model Semantics (A Review)
19.2.1 Definitions: Causal Models, Actions and Counterfactuals
19.2.2 Examples
19.2.3 Relation to Lewis' Counterfactuals
19.2.4 Relation to Probabilistic Causality
19.2.5 Relation to Neyman-Rubin Model
19.3 Necessary and Sufficient Causes: Conditions of Identification
19.3.1 Definitions, Notations, and Basic Relationships
19.3.2 Bounds and Basic Relationships under Exogeneity
19.3.3 Identifiability under Monotonicity and Exogeneity
19.3.4 Identifiability under Monotonicity and Non-Exogeneity
19.4 Examples and Applications
19.4.1 Example 1: Betting against a Fair Coin
19.4.2 Example 2: The Firing Squad
19.4.3 Example 3: The Effect of Radiation on Leukemia
19.4.4 Example 4: Legal Responsibility from Experimental and Nonexperimental Data
19.5 Identification in Non-Monotonic Models
19.6 From Necessity and Sufficiency to "Actual Cause"
19.6.1 The Role of Structural Information
19.6.2 Singular Sufficient Causes
19.6.3 Example: The Desert Traveler (after P. Suppes)
19.6.3.1 Necessity and Sufficiency Ignoring Internal Structure
19.6.3.2 Sufficiency and Necessity given Forensic Reports
19.6.3.3 Necessity Given Forensic Reports
19.7 Conclusion
19.A Appendix: The Empirical Content of Counterfactuals
References
20 Direct and Indirect Effects
Abstract
20.1 Introduction
20.2 Conceptual Analysis
20.2.1 Direct versus Total Effects
20.2.2 Descriptive versus Prescriptive Interpretation
20.2.3 Policy Implications of the Descriptive Interpretation
20.2.4 Descriptive Interpretation of Indirect Effects
20.3 Formal Analysis
20.3.1 Notation
20.3.2 Controlled Direct Effects (review).
20.3.3 Natural Direct Effects: Formulation.