Causal Inference in Statistics – A Primer / Judea Pearl, Madelyn Glymour, Nicholas P. Jewell
SYSNO 6468588, přírůstkové číslo 7386


Seznam obrázků v dokumentu:
Figure 1.1 Results of the exercise-cholesterol study, segregated by age
Figure 1.2 Results of the exercise-cholesterol study, unsegregated. The data points are identi-cal to those of Figure 1.1, except the boundaries between the various age groups are not shown
Figure 1.3 Scatter plot of the results in Table 1.6, with the value of Die 1 on the x-axis and the sum of the two dice rolls on the y-axis
Figure 1.4 Scatter plot of the results in Table 1.6, with the value of Die 1 on the x-axis and the sum of the two dice rolls on the y-axis. The dotted line represents the line of best fit based on the data. The solid line represents the line of best fit we would expect in the popula-tion
Figure 1.5 An undirected graph in which nodes X and Y are adjacent and nodes Y and Z are adjacent but not X and Z
Figure 1.6 A directed graph in which node A is a parent of B and B is a parent of C
Figure 1.7 (a) Showing acyclic graph and (b) cyclic graph
Figure 1.8 A directed graph used in Study question 1.4.1
Figure 1.9 The graphical model of SCM 1.5.1, with X indicating years of schooling, Y indicat-ing years of employment, and Z indicating salary
Figure 1.10 Model showing an unobserved syndrome, Z, affecting both treatment (X) and outcome (Y)
Figure 2.1 The graphical model of SCMs 2.2.1–2.2.3
Figure 2.2 The graphical model of SCMs 2.2.5 and 2.2.6
Figure 2.3 A simple collider
Figure 2.4 A simple collider, Z, with one child, W, representing the scenario from Table 2.3, with X representing one coin flip, Y representing the second coin flip, Z representing a bell that rings if either X or Y is heads, and W representing an unreliable witness who reports on wheth-er or not the bell has rung
Figure 2.5 A directed graph for demonstrating conditional independence (error terms are not shown explicitly
Figure 2.6 A directed graph in which P is a descendant of a collider
Figure 2.7 A graphical model containing a collider with child and a fork
Figure 2.8 The model from Figure 2.7 with an additional forked path between Z and Y.
Figure 2.9 A causal graph used in study question 2.4.1, all U terms (not shown) are assumed independent
Figure 3.1 A graphical model representing the relationship between temperature (Z), ice cream sales (X), and crime rates (Y)
Figure 3.2 A graphical model representing an intervention on the model in Figure 3.1 that lowers ice cream sales
Figure 3.3 A graphical model representing the effects of a new drug, with Z representing gender, X standing for drug usage, and Y standing for recovery
Figure 3.4 A modified graphical model representing an intervention on the model in Figure 3.3 that sets drug usage in the population, and results in the manipulated probability Pm
Figure 3.5 A graphical model representing the effects of a new drug, with X representing drug usage, Y representing recovery, and Z representing blood pressure (measured at the end of the study). Exogenous variables are not shown in the graph, implying that they are mutually independent
Figure 3.6 A graphical model representing the relationship between a new drug (X), recovery (Y), weight (W), and an unmeasured variable Z (socioeconomic status)
Figure 3.7 A graphical model in which the backdoor criterion requires that we condition on a collider (Z) in order to ascertain the effect of X on Y
Figure 3.8 Causal graph used to illustrate the backdoor criterion in the following study ques-tions
Figure 3.9 Scatter plot with students’ initial weights on the x-axis and final weights on the y-axis. The vertical line indicates students whose initial weights are the same, and whose final weights are higher (on average) for plan B compared with plan A
Figure 3.10 A graphical model representing the relationships between smoking (X) and lung cancer (Y), with unobserved confounder (U) and a mediating variable Z
Figure 3.11 A graphical model representing the relationship between gender, qualifications, and hiring
Figure 3.12 A graphical model representing the relationship between gender, qualifications, and hiring, with socioeconomic status as a mediator between qualifications and hiring
Figure 3.13 A graphical model illustrating the relationship between path coefficients and total effects
Figure 3.14 A graphical model in which X has no direct effect on Y, but a total effect that is determined by adjusting for T
Figure 3.15 A graphical model in which X has direct effect ? on Y
Figure 3.16 By removing the direct edge from X to Y and finding the set of variables {W} that d-separate them, we find the variables we need to adjust for to determine the direct effect of X on Y
Figure 3.17 A graphical model in which we cannot find the direct effect of X on Y via ad-justment, because the dashed double-arrow arc represents the presence of a backdoor path between X and Y, consisting of unmeasured variables. In this case, Z is an instrument with regard to the effect of X on Y that enables the identification of ?
Figure 3.18 Graph corresponding to Model 3.1 in Study question 3.8.1
Figure 4.1 A model depicting the effect of Encouragement (X) on student’s score
Figure 4.2 Answering a counterfactual question about a specific student’s score, predicated on the assumption that homework would have increased to H =2
Figure 4.3 A model representing Eq. (4.7), illustrating the causal relations between college education (X), skills (Z), and salary (Y)
Figure 4.4 Illustrating the graphical reading of counterfactuals. 
Figure 4.5 (a) Showing how probabilities of necessity (PN) are bounded, as a function of the excess risk ratio (ERR) and the confounding factor (CF) (Eq. (4.31)); (b) showing how PN is identified when monotonicity is assumed (Theorem 4.5.1)
Figure 4.6 (a) The basic nonparametric mediation model, with no confounding. (b) A con-founded mediation model in which dependence exists between UM and (UT, UY)