Cover	1
	Title Page	5
	Copyright	6
	Dedication	7
	Contents	9
	About the Authors	11
	Preface	13
	List of Figures	17
	About the Companion Website	21
	Chapter 1 Preliminaries: Statistical and Causal Models	23
	1.1 Why Study Causation	23
	1.2 Simpson's Paradox	23
	1.3 Probability and Statistics	29
	1.3.1 Variables	29
	1.3.2 Events	30
	1.3.3 Conditional Probability	30
	1.3.4 Independence	32
	1.3.5 Probability Distributions	33
	1.3.6 The Law of Total Probability	33
	1.3.7 Using Bayes' Rule	35
	1.3.8 Expected Values	38
	1.3.9 Variance and Covariance	39
	1.3.10 Regression	42
	1.3.11 Multiple Regression	44
	1.4 Graphs	46
	1.5 Structural Causal Models	48
	1.5.1 Modeling Causal Assumptions	48
	1.5.2 Product Decomposition	51
	Chapter 2 Graphical Models and Their Applications	57
	2.1 Connecting Models to Data	57
	2.2 Chains and Forks	57
	2.3 Colliders	62
	2.4 d-separation	67
	2.5 Model Testing and Causal Search	70
	Chapter 3 The Effects of Interventions	75
	3.1 Interventions	75
	3.2 The Adjustment Formula	77
	3.2.1 To Adjust or not to Adjust?	80
	3.2.2 Multiple Interventions and the Truncated Product Rule	82
	3.3 The Backdoor Criterion	83
	3.4 The Front-Door Criterion	88
	3.5 Conditional Interventions and Covariate-Specific Effects	92
	3.6 Inverse Probability Weighing	94
	3.7 Mediation	97
	3.8 Causal Inference in Linear Systems	100
	3.8.1 Structural versus Regression Coefficients	102
	3.8.2 The Causal Interpretation of Structural Coefficients	103
	3.8.3 Identifying Structural Coefficients and Causal Effect	105
	3.8.4 Mediation in Linear Systems	109
	Chapter 4 Counterfactuals and Their Applications	111
	4.1 Counterfactuals	111
	4.2 Defining and Computing Counterfactuals	113
	4.2.1 The Structural Interpretation of Counterfactuals	113
	4.2.2 The Fundamental Law of Counterfactuals	115
	4.2.3 From Population Data to Individual Behavior-An Illustration	116
	4.2.4 The Three Steps in Computing Counterfactuals	118
	4.3 Nondeterministic Counterfactuals	120
	4.3.1 Probabilities of Counterfactuals	120
	4.3.2 The Graphical Representation of Counterfactuals	123
	4.3.3 Counterfactuals in Experimental Settings	125
	4.3.4 Counterfactuals in Linear Models	128
	4.4 Practical Uses of Counterfactuals	129
	4.4.1 Recruitment to a Program	129
	4.4.2 Additive Interventions	131
	4.4.3 Personal Decision Making	133
	4.4.4 Sex Discrimination in Hiring	135
	4.4.5 Mediation and Path-disabling Interventions	136
	4.5 Mathematical Tool Kits for Attribution and Mediation	138
	4.5.1 A Tool Kit for Attribution and Probabilities of Causation	138
	4.5.2 A Tool Kit for Mediation	142
	References	149
	Index	155
	EULA	159