Causal Concepts, Principles, and Algorithms

  • Louis Anthony Cox Jr.
  • Douglas A. Popken
  • Richard X. Sun
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 270)


It is an important truism that association is not causation. For example, people living in low-income areas may have higher levels of exposure to an environmental hazard and also higher levels of some adverse health effect than people living in wealthier areas. Yet this observed association, no matter how strong, consistent, statistically significant, biologically plausible, and well documented by multiple independent teams, does not necessarily tell a policy maker anything about whether or by how much a proposed costly reduction in exposure would reduce adverse health effects. Perhaps only increasing income, or something that income can buy, would reduce adverse health effects. Or maybe factors that cannot be changed by policy interventions increase both the probability of living in low-income areas and the probability of adverse health effects. Whatever the truth is about opportunities to improve health by changing policy variables, it typically cannot be determined by studying correlations, regression coefficients, relative risks, or other measures of association between exposures and health effects (Pearl 2009). Observed associations between variables can contain both causal and non-causal (“spurious”) components. In general, the effects of policy changes on outcomes of interest can only be predicted and evaluated correctly by modeling the network of causal relationships by which effects of exogenous changes propagate among variables. The chapter reviews current causal concepts, principles, and algorithms for carrying out such causal modeling and compares them to other approaches.


  1. Andreassen S, Hovorka R, Benn J, Olesen KG, Carson ER (1991) A model-based approach to insulin adjustment. In: Proceedings of AIME’91, pp 239–248CrossRefGoogle Scholar
  2. Angrist JD, Imbens GW, Rubin DB (1996) Identification of causal effects using instrumental variables. J Am Stat Assoc 91(434):444–455CrossRefGoogle Scholar
  3. Apte JS, Marshall JD, Cohen AJ, Brauer M (2015) Addressing global mortality from Ambient PM2.5. Environ Sci Technol 49(13):8057–8066CrossRefGoogle Scholar
  4. Aragam B, Gu J, Zhou Q (2017) Learning large-scale Bayesian networks with the sparsebn package. arXiv: 1703.04025. Accessed 19 Dec 2017
  5. Asghar N (2016) Automatic extraction of causal relations from natural language texts: a comprehensive survey. Accessed 19 Dec 2017
  6. Azzimonti L, Corani G, Zaffalon M (2017) Hierarchical Multinomial-Dirichlet model for the estimation of conditional probability tables. Accessed 18 November 2017
  7. Bareinboim E, Pearl J (2013) Causal transportability with limited experiments. In: Proceedings of the 27th AAAI conference on artificial intelligence, pp 95–101.
  8. Barnett L, Seth AK (2014) The MVGC multivariate granger causality toolbox: a new approach to granger-causal inference. J Neurosci Methods 223:50–68CrossRefGoogle Scholar
  9. Bartholomew MJ, Vose DJ, Tollefson LR, Travis CC (2005) A linear model for managing the risk of antimicrobial resistance originating in food animals. Risk Anal 25(1):99–108CrossRefGoogle Scholar
  10. Bearfield G, Marsh W (2005) Generalising event trees using bayesian networks with a case study of train derailment. In: Winther R, Gran BA, Dahll G (eds) Computer safety, reliability, and security. SAFECOMP 2005, Lecture notes in computer science, vol 3688. Springer, Berlin, HeidelbergGoogle Scholar
  11. Blalock HM (1964) Causal inferences in nonexperimental research. The University of North Carolina Press, Chapel Hill, NCGoogle Scholar
  12. Bobbio A, Portinale L, Minichino M, Ciancamerla E (2001) Improving the analysis of dependable systems by mapping fault trees into Bayesian networks. Reliab Eng Syst Saf 71:249–260CrossRefGoogle Scholar
  13. Bontempi G, Flauder M (2015) From dependency to causality: a machine learning approach. J Mach Learn Res 16:2437–2457Google Scholar
  14. Boutilier C, Dearden R, Goldszmidt M (1995) Exploiting structure in policy construction. In: Proceedings of the 14th international joint conference on artificial intelligence, Montreal, QC, Canada, pp 1104–1113Google Scholar
  15. Brewer LE, Wright JM, Rice G, Neas L, Teuschler L (2017) Causal inference in cumulative risk assessment: the roles of directed acyclic graphs. Environ Int 102:30–41. Scholar
  16. Breiman L, Friedman JH, Olshen RA, Stone CJ (1984) Classification and regression trees. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  17. Campbell DT, Stanley JC (1963) Experimental and quasi-experimental designs for research. Houghton Mifflin Company, Boston, MAGoogle Scholar
  18. Charniak E (1991) Bayesian networks without tears. AI Mag 12(1):50–63. Scholar
  19. Clancy L, Goodman P, Sinclair H, Dockery DW (2002) Effect of air-pollution control on death rates in Dublin, Ireland: an intervention study. Lancet 360(9341):1210–1214CrossRefGoogle Scholar
  20. Cole SR, Platt RW, Schisterman EF, Chu H, Westreich D, Richardson D, Poole C (2010) Illustrating bias due to conditioning on a collider. Int J Epidemiol 39(2):417–420CrossRefGoogle Scholar
  21. Cossalter M, Mengshoel O, Selker T (2011) Visualizing and understanding large-scale Bayesian networks. In: Proceedings of the 17th AAAI conference on scalable integration of analytics and visualization, AAAI Press, pp 12–21Google Scholar
  22. Cover TM, Thomas JA (2006) Elements of information theory, 2nd edn. Wiley, Hoboken, NJ. ISBN-13 978-0-471-24195-9. ISBN-10 0-471-24195-4. Accessed 9 Jan 2018Google Scholar
  23. Cox LA Jr (2017a) Do causal concentration-response functions exist? A critical review of associational and causal relations between fine particulate matter and mortality. Crit Rev Toxicol 47(7):603–631. Scholar
  24. Cox LA Jr (2017b) Socioeconomic and air pollution correlates of adult asthma, heart attack, and stroke risks in the United States, 2010-2013. Environ Res 155:92–107. Scholar
  25. Cox LA Jr (1984) Probability of causation and the attributable proportion of risk. Risk Anal 4:221–230. Scholar
  26. Cox LA Jr (1987) Statistical issues in the estimation of assigned shares for carcinogenesis liability. Risk Anal 7(1):71–80CrossRefGoogle Scholar
  27. Crowley M (2004) Evaluating influence diagrams.
  28. Di Q, Wang Y, Zanobetti A, Wang Y, Koutrakis P, Dominici F, Schwartz JD (2017) Association of short-term exposure to air pollution with mortality in older adults. J Am Med Assoc 318(24):2446–2456CrossRefGoogle Scholar
  29. Ding P (2017) A paradox from randomization-based causal inference. Statist Sci 32(3):331–345. Scholar
  30. Dockery DW, Rich DQ, Goodman PG, Clancy L, Ohman-Strickland P, George P, Kotlov T, HEI Health Review Committee (2013) Effect of air pollution control on mortality and hospital admissions in Ireland. Res Rep Health Eff Inst 176:3–109Google Scholar
  31. Dominici F, Zigler C (2017) Best practices for gauging evidence of causality in air pollution epidemiology. Am J EpidemiolGoogle Scholar
  32. Dockery D, Pope C, Xu X et al (1993) An association between air pollution and mortality in six US cities. N Engl J Med 329:1753–1759CrossRefGoogle Scholar
  33. Druzdzel MJ, Simon H (1993) Causality in bayesian belief networks. In: UAI’93 proceedings of the ninth international conference on uncertainty in artificial intelligence, Washington, DC, 9–11 July 1993. Morgan Kaufmann Publishers Inc., San Francisco, CA, pp 3–11CrossRefGoogle Scholar
  34. Dugan JB (2000) Galileo: a tool for dynamic fault tree analysis. In: Haverkort BR, Bohnenkamp HC, Smith CU (eds) Computer performance evaluation. Modelling techniques and tools. TOOLS 2000. Lecture Notes in Computer Science, vol 1786. Springer, Berlin, HeidelbergGoogle Scholar
  35. Fann N, Lamson AD, Anenberg SC, Wesson K, Risley D, Hubbell BJ (2012) Estimating the national public health burden associated with exposure to ambient PM2.5 and ozone. Risk Anal 32(1):81–95CrossRefGoogle Scholar
  36. Franklin M, Zeka A, Schwartz J (2006) Association between PM2.5 and all-cause and specific-cause mortality in 27 US communities. J Expo Sci Environ Epidemiol 17:279–287CrossRefGoogle Scholar
  37. Frey L, Fisher D, Tsamardinos I, Aliferis CF, Statnikov A (2003) Identifying Markov blankets with decision tree induction. In: Proceedings of the third IEEE international conference on data mining, Melbourne, FL, 19–22 Nov 2003. pp 59–66Google Scholar
  38. Friston K, Moran R, Seth AK (2013) Analyzing connectivity with Granger causality and dynamic causal modelling. Curr Opin Neurobiol 23(2):172–178CrossRefGoogle Scholar
  39. Funk MJ, Westreich D, Wiesen C, Stürmer T, Brookhart MA, Davidian M (2011) Doubly robust estimation of causal effects. Am J Epidemiol 173(7):761–767. Scholar
  40. Furgan MS, Sival MY (2016) Inference of biological networks using Bi-directional Random Forest Granger causality. Springerplus 5(514).
  41. Gamble JF (2011) Crystalline silica and lung cancer: a critical review of the occupational epidemiology literature of exposure-response studies testing this hypothesis. Crit Rev Toxicol 41(5):404–465. Scholar
  42. Gharamani Z (2001) An introduction to Hidden Markov models and Bayesian networks. Int J Pattern Recognit Artif Intell 15(1):9–42. Scholar
  43. Giannadaki D, Lelieveld J, Pozzer A (2016) Implementing the US air quality standard for PM2.5 worldwide can prevent millions of premature deaths per year. Environ Health 15(1):88CrossRefGoogle Scholar
  44. Glass TA, Goodman SN, Hernán MA, Samet JM (2013) Causal inference in public health. Annu Rev Public Health 34:61–75. Scholar
  45. Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37(3):424–438CrossRefGoogle Scholar
  46. Greenland S (2015) Concepts and pitfalls in measuring and interpreting attributable fractions, prevented fractions, and causation probabilities. Ann Epidemiol 25(3):155–161. Scholar
  47. Hart J, Garshick E, Dockery D, Smith T, Ryan L, Laden F (2011) Long-term ambient multi-pollutant exposures and mortality. Am J Respir Crit Care Med 183:73–78CrossRefGoogle Scholar
  48. Hausman DM, Woodward J (2004) Modularity and the causal markov condition: a restatement. Br J Philos Sci 55(1):147–161. Scholar
  49. Hausman DM, Woodward J (1999) Independence, invariance, and the Causal Markov condition. Br J Philos Sci 50(4):521 583. Scholar
  50. Heinze-Deml C, Peters J, Meinshausen N (2017) Invariant causal prediction for nonlinear models.
  51. Hernan M, VanderWeele T (2011) On compound treatments and transportability of causal inference. Epidemiology 22:368CrossRefGoogle Scholar
  52. Hill AB (1965) The environment and disease: association or causation? Proc R Soc Med 58:295–300Google Scholar
  53. Hill J (2016) Atlantic causal inference conference competition: IS your SATT where it’s at?
  54. Höfler M (2005) The Bradford Hill considerations on causality: a counterfactual perspective. Emerg Themes Epidemiol 2:11CrossRefGoogle Scholar
  55. Holt J, Leach AW, Johnson S, Tu DM, Nhu DT, Anh NT, Quinlan MM, Whittle PJL, Mengersen K, Mumford JD (2017) Bayesian networks to compare pest control interventions on commodities along agricultural production chains. Risk Anal.
  56. Hoover KD (2012) Causal structure and hierarchies of models. Stud History Philos Sci C 43(4):778–786. Scholar
  57. IARC (2006) IARC monographs on the evaluation of carcinogenic risk to humans: preamble. International Agency for Research on Cancer (IARC), Lyons, France. Scholar
  58. Imai K, Keele L, Tingley D, Yamamoto T (2011) Unpacking the black box of causality: learning about causal mechanisms from experimental and observational studies. Am Polit Sci Rev 4:105Google Scholar
  59. Iserman R, Münchhof M (2011) Identification of dynamic systems: an introduction with applications. Springer, New York, NYCrossRefGoogle Scholar
  60. Jonsson A, Barto B (2007) Active learning of dynamic Bayesian networks in Markov decision processes. In: SARA’07 proceedings of the 7th international conference on abstraction, reformulation, and approximation, Whistler, Canada, 18–21 July 2007. Springer, Berlin, pp 273–284Google Scholar
  61. Kahneman D (2011) Thinking fast and slow. Farrar, Straus, and Giroux, New YorkGoogle Scholar
  62. Khakzad N, Reniers G (2015) Risk-based design of process plants with regard to domino effects and land use planning. J Hazard Mater 299:289–297. Scholar
  63. Keele L, Tingley D, Yamamoto T (2015) Identifying mechanisms behind policy interventions via causal mediation analysis. J Policy Anal Manage 34(4):937–963CrossRefGoogle Scholar
  64. Kenny DA (1979) Correlation and causality. Wiley, New YorkGoogle Scholar
  65. Khakzad N, Khan F, Amyotte P (2013) Dynamic safety analysis of process systems by mapping bow-tie into Bayesian network. Process Saf Environ Prot 91(1–2):46–53CrossRefGoogle Scholar
  66. Kleinberg S, Hripcsak G (2011) A review of causal inference for biomedical informatics. J Biomed Inform 44(6):1102–1112CrossRefGoogle Scholar
  67. Koller D, Friedman N (2009) Probabilistic graphical models: principles and techniques. MIT Press, Cambridge, MAGoogle Scholar
  68. Kuhn M (2008) Building predictive models in R using the caret package. J Stat Softw 28(5):1–26. Scholar
  69. Lähdesmäki H, Hautaniemi S, Shmulevich I, Yli-Hari O (2006) Relationships between probabilistic Boolean networks and dynamic Bayesian networks as models of gene regulatory networks. Signal Process 86(4):814–834. Scholar
  70. Lagani V, Triantafillou S, Ball G, Tegnér J, Tsamardinos I. (2016) Chapter 2: probabilistic computational causal discovery for systems biology. In: Geris L, Gomez-Cabrero D (eds) Uncertainty in biology: a computational modeling approach. SpringerGoogle Scholar
  71. Lee S, Honavar V (2013) m-transportability: transportability of a causal effect from multiple environments. In: Proceedings of the twenty-seventh AAAI conference on artificial intelligence. (Bareinboim and Pearl, 2013; Lee and Honavar, 2013)
  72. Leu SS, Chang CM (2013) Bayesian-network-based safety risk assessment for steel construction projects. Accid Anal Prev 54:122–133. Scholar
  73. Lepeule J, Laden F, Dockery D, Schwartz J (2012) Chronic exposure to fine particles and mortality: an extended follow-up of the Harvard Six Cities study from 1974 to 2009. Environ Health Perspect 120:965–970CrossRefGoogle Scholar
  74. Li J, Ma S, Le T, Liu L, Liu J (2017) Causal decision trees. IEEE Trans Knowl Data Eng 29(2):257–271CrossRefGoogle Scholar
  75. Lo WC, Shie RH, Chan CC, Lin HH (2016) Burden of disease attributable to ambient fine particulate matter exposure in Taiwan. J Formos Med Assoc 116(1):32–40CrossRefGoogle Scholar
  76. Lok JJ (2017) Mimicking counterfactual outcomes to estimate causal effects. Ann Stat 45(2):461–499. Scholar
  77. Machado D, Costa RS, Rocha M, Ferreira EC, Tidor B, Rocha I (2011) Modeling formalisms in systems biology. AMB Express 1:45. Scholar
  78. Maglogiannis I, Zafiropoulos E, Platis A, Lambrinoudakis C (2006) Risk analysis of a patient monitoring system using Bayesian network modeling. J Biomed Inform 39(6):637–647CrossRefGoogle Scholar
  79. Maldonado G (2013) Toward a clearer understanding of causal concepts in epidemiology. Ann Epidemiol 23(12):743–749CrossRefGoogle Scholar
  80. Mauá DD (2016) Equivalences between maximum a posteriori inference in Bayesian networks and maximum expected utility computation in influence diagrams. Int J Approx Reason 68(C):211–229CrossRefGoogle Scholar
  81. McClellan RO (1999) Human health risk assessment: a historical overview and alternative paths forward. Inhal Toxicol 11(6–7):477–518CrossRefGoogle Scholar
  82. Mengshoel OJ, Chavira M, Cascio K, Poll S, Darwiche A, Uckun S (2010) Probabilistic model-based diagnosis: an electrical power system case study. IEEE Trans Syst Man Cybern Part A Syst Hum 40(5):874–885CrossRefGoogle Scholar
  83. Menzies P (2012) The causal structure of mechanisms. Stud Hist Phil Biol Biomed Sci 43(4):796–805. Scholar
  84. Murray CJ, Lopez AD (2013) Measuring the global burden of disease. N Engl J Med 369(5):448–457. Scholar
  85. Nadkarni S, Shenoy PP (2004) A causal mapping approach to constructing Bayesian networks. Decis Support Syst 38(2):259–281. Scholar
  86. National Research Council (2012) Deterrence and the death penalty. Washington, DC: The National Academies Press. doi: Scholar
  87. Ogarrio JM, Spirtes P, Ramsey J (2016) A hybrid causal search algorithm for latent variable models. JMLR Workshop Conf Proc 52:368–379. Scholar
  88. Neyman J (1923) Sur les applications de la theorie des probabilites aux experiences agricoles: Essai des principes. Master’s thesis (trans: Dabrowska DM, Speed TP) Excerpts reprinted in English, Statistical Science, vol 5, pp 463–472Google Scholar
  89. Nowzohour C, Bühlmann P (2016) Score based causal learning in additive noise models. Statistics 50(3):471–485CrossRefGoogle Scholar
  90. Omenn GS, Goodman GE, Thornquist MD, Balmes J, Cullen MR, Glass A, Keogh JP, Meyskens FL, Valanis B, Williams JH, Barnhart S, Hammar S (1996) Effects of a combination of beta carotene and vitamin A on lung cancer and cardiovascular disease. N Engl J Med 334(18):1150–1155CrossRefGoogle Scholar
  91. Pang M, Schuster T, Filion KB, Schnitzer ME, Eberg M, Platt RW (2016) Effect estimation in point-exposure studies with binary outcomes and high-dimensional covariate data—a comparison of targeted maximum likelihood estimation and inverse probability of treatment weighting. Int J Biostat 12(2).
  92. Papana A, Kyrtsou C, Kugiumtzis D, Diks C (2017) Assessment of resampling methods for causality testing: a note on the US inflation behavior. PLoS One 12(7):e0180852. Scholar
  93. Pearl J (1993) Comment: graphical models, causality and intervention. Stat Sci 8:266–2669 Scholar
  94. Pearl J (2000) Causality: models, reasoning, and inference. Cambridge University Press, CambridgeGoogle Scholar
  95. Pearl J (2001) Direct and indirect effects. In: Proceedings of the seventeenth conference on uncertainty in artificial intelligence, Morgan Kaufmann, San Francisco, CA, pp 411–420Google Scholar
  96. Pearl J (2009) Causal inference in statistics: an overview. Stat Surv 3:96–146. Scholar
  97. Pearl J (2010) An introduction to causal inference. Int J Biostat 6(2):7CrossRefGoogle Scholar
  98. Pearl J (2014) Reply to commentary by Imai, Keele, Tingley, and Yamamo to concerning causal mediation analysis. Psychol Methods 19(4):488–492CrossRefGoogle Scholar
  99. Peters J, Bühlmann P, Meinshausen N (2016) Causal inference using invariant prediction: identification and confidence intervals. J R Stat Soc Ser B 78(5):947–1012CrossRefGoogle Scholar
  100. Petersen ML, Sinisi SE, van der Laan MJ (2006) Estimation of direct causal effects. Epidemiology 17(3):276–284CrossRefGoogle Scholar
  101. Peyrard N, Givry S, Franc A, Robin S, Sabbadin R, Schiex T, Vignes M (2015) Exact and approximate inference in graphical models: Variable elimination and beyond.
  102. Poole DL, Mackworth AK (2017) Artificial intelligence: foundations of computational agents, 2nd edn. Cambridge University Press.
  103. Prüss-Üstün A, Mathers C, Corvalán C, Woodward A (2003) Introduction and methods: Assessing the environmental burden of disease at national and local levels, Environmental burden of disease series No. 1. World Health Organization (WHO), Geneva, Switzerland. Scholar
  104. Relton C, Torgerson D, O’Cathain A, Nicholl J (2010) Rethinking pragmatic randomised controlled trials: introducing the “cohort multiple randomised controlled trial” design. BMJ 340:c1066. Scholar
  105. Rhomberg LR, Chandalia JK, Long CM, Goodman JE (2011) Measurement error in environmental epidemiology and the shape of exposure-response curves. Crit Rev Toxicol 41(8):651–671. Scholar
  106. Richardson TS, Rotnitzky A (2014) Causal etiology of the research of James M. Robins. Stat Sci 29(4):459–484. Scholar
  107. Rigaux C, Ancelet S, Carlin F, Nguyen-thé C, Albert I (2013) Inferring an augmented Bayesian network to confront a complex quantitative microbial risk assessment model with durability studies: application to Bacillus cereus on a courgette purée production chain. Risk Anal 33(5):877–892. Scholar
  108. Robins JM, Greenland S (1992) Identifiability and exchangeability for direct and indirect effects. Epidemiology 3:143–155CrossRefGoogle Scholar
  109. Rosenbaum P, Rubin D (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70(1):41–55. Scholar
  110. Rothenhausler D, Heinze C, Peters J, Meinschausen N (2015) BACKSHIFT: learning causal cyclic graphs from unknown shift interventions. arXiv pre-print See also the BACKSHIFT R package at
  111. Rubin D (1974) Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol 66(5):688–701CrossRefGoogle Scholar
  112. Rubin D (1978) Bayesian inference for causal effects: the role of randomization. Ann Stat 6:34–58CrossRefGoogle Scholar
  113. Rubin DB (2004) Direct and indirect causal effects via potential outcomes. Scand J Stat 31:161–170CrossRefGoogle Scholar
  114. Sanchez-Graillet O, Poesio M (2004) Acquiring Bayesian networks from text. In: Proceedings of the fourth international conference on language resources and evaluation (LREC’04), Lisbon, Portugal, May 26–28. European Language Resources Association (ELRA), Paris, France.
  115. Savageau M, Voit E (1987) Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Math Biosci 87(1):83–115CrossRefGoogle Scholar
  116. Schaffter T, Marbach D, Floreano D (2011) GeneNetWeaver: in silico benchmark generation and performance profiling of network inference methods. Bioinformatics 27(16):2263–2270CrossRefGoogle Scholar
  117. Schreiber T (2000) Measuring information transfer. Phys Rev Lett 85(2):461–464. Scholar
  118. Shachter RD (1986) Evaluating influence diagrams. Oper Res 34(6):871–882CrossRefGoogle Scholar
  119. Shachter RD, Bhattacharjya D (2010) Solving influence diagrams: exact algorithms. In: Cochran J et al (eds) Wiley encyclopedia of operations research and management science. Wiley, New York. Scholar
  120. Schwartz S, Gatto NM, Campbell UB (2011) Transportabilty and causal generalization. Epidemiology 22(5):745–746CrossRefGoogle Scholar
  121. Schwartz J, Laden F, Zanobetti A (2002) The concentration-response relation between PM(2.5) and daily deaths. Environ Health Perspect 110(10):1025–1029CrossRefGoogle Scholar
  122. Shimizu S, Hoyer PO, Hyvarinen A, Kerminen A (2006) A linear non-Gaussian acyclic model for causal discovery. J Mach Learn Res 7:2003–2030Google Scholar
  123. Shpitser I, Pearl J (2008) Complete identification methods for the causal hierarchy. J Mach Learn Res 9(Sep):1941–1979Google Scholar
  124. Simon HA (1953) Chapter III: Causal ordering and identifiability. In: Hood WC, Koopmans TC (eds) Studies in econometric method, Cowles Commission for Research in Economics Monograph No. 14. Wiley, New York, NY, pp 49–74Google Scholar
  125. Simon HA (1954) Spurious correlation: a causal interpretation. J Am Stat Assoc 49(267):467–479Google Scholar
  126. Simon HA, Iwasaki Y (1988) Causal ordering, comparative statics, and near decomposability. J Econ 39:149–173. Scholar
  127. Spitz MR, Hong WK, Amos CI, Wu X, Schabath MB, Dong Q, Shete S, Etzel CJ (2007) A risk model for prediction of lung cancer. J Natl Cancer Inst 99(9):715–726CrossRefGoogle Scholar
  128. Suppes P (1970) A probabilistic theory of causality. North-Holland Publishing Company, Amsterdam, HollandGoogle Scholar
  129. Tashiro T, Shimizu S, Hyvärinen A, Washio T (2014) ParceLiNGAM: a causal ordering method robust against latent confounders. Neural Comput 26(1):57–83. Scholar
  130. Textor J, van der Zander B, Gilthorpe MS, Liskiewicz M, Ellison GT (2016) Robust causal inference using directed acyclic graphs: the R package ‘dagitty’. Int J Epidemiol 45(6):1887–1894Google Scholar
  131. Theocharous G, Murphy K, Kaelbling LP (2004) Representing hierarchical POMDPs as DBNs for multi-scale robot localization. In: Proceedings of the IEEE international conference on robotics and automation ICRA’04Google Scholar
  132. Triantafillou S, Tsamardinos I (2015) Constraint-based causal discovery from multiple interventions over overlapping variable sets. J Mach Learn Res 16:2147–2205Google Scholar
  133. Trovati M (2015) Extraction of Bayesian networks from large unstructured datasets. In: Trovati M, Hill R, Anjum A, Zhu S, Liu L (eds) Big-data analytics and cloud computing. Springer, ChamCrossRefGoogle Scholar
  134. Tudor RS, Hovorka R, Cavan DA, Meeking D, Hejlesen OK, Andreassen S (1998) DIAS-NIDDM—a model-based decision support system for insulin dose adjustment in insulin-treated subjects with NIDDM. Comput Methods Prog Biomed 56(2):175–191CrossRefGoogle Scholar
  135. VanderWeele TJ, Vansteelandt S (2009) Conceptual issues concerning mediation, interventions and composition. Stat Its Interface 2:457–468CrossRefGoogle Scholar
  136. Voortman M, Dash D, Druzdzel MJ (2010) Learning causal models that make correct manipulation predictions with time series data. Proc Mach Learn Res 6:257–266. Scholar
  137. Vrignat P, Avila M, Duculty F, Kratz F (2015) Failure event prediction using Hidden Markov Model approaches. IEEE Trans Reliab 99:1–11Google Scholar
  138. Westreich D (2012) Berkson’s bias, selection bias, and missing data. Epidemiology 23(1):159–164. Scholar
  139. Wibral M, Pampu N, Priesemann V, Siebenhuhner F, Seiwert H, Lindner M, Lizier JT, Vicente R (2013) Measuring information-transfer delays. PLoS One 8(2):e55809. Scholar
  140. Wintle BC, Nicholson A (2014) Exploring risk judgments in a trade dispute using Bayesian networks. Risk Anal 34(6):1095–1111. Scholar
  141. Wickham H (2014) Tidy data. J Stat Softw 59(10):1–23CrossRefGoogle Scholar
  142. Wiener N (1956) The theory of prediction. In: Beckenbach EF (ed) Modern mathematics for engineers, vol 1. McGraw-Hill, New YorkGoogle Scholar
  143. Wright S (1921) Correlation and causation. J Agric Res 20:557–585. Scholar
  144. Wu AH, Yu MC, Thomas DC, Pike MC, Henderson BE (1988) Personal and family history of lung disease as risk factors for adenocarcinoma of the lung. Cancer Res 48(24 Pt 1):7279–7284Google Scholar
  145. Zhang J (2008) On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias. Artif Intell 172(16–17):1873–1896CrossRefGoogle Scholar
  146. Zhang JL, Rubin DB (2003) Estimation of causal effects via principal stratification when some outcomes are truncated by “death”. J Educ Behav Stat 28:353–368. Scholar
  147. Zhang L, Wu X, Qin Y, Skibniewski MJ, Liu W (2016) Towards a fuzzy Bayesian network based approach for safety risk analysis of tunnel-induced pipeline damage. Risk Anal 36(2):278–301. Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Louis Anthony Cox Jr.
    • 1
  • Douglas A. Popken
    • 2
  • Richard X. Sun
    • 3
  1. 1.Cox AssociatesDenverUSA
  2. 2.Cox AssociatesLittletonUSA
  3. 3.Cox AssociatesEast BrunswickUSA

Personalised recommendations