Inferring cause and effect from nature, especially from observational (as opposed to ideal experimental) data where it is hard.
Graphical models and related techniques for doing it.
Avoiding the danger of folk statistics.
Observational studies, confounding, adjustment criteria, *d*-separation,
identifiability, interventions, moral equivalence…
Avoidance of Ecological fallacy/
Simpson’s paradox.

The gold standard, of course, is to work out if A causes B by doing an experiment where no input but A changes, then observing B, which is what a controlled trial is.
In practice this is unattainable because it would usually require cloning the entire state of the universe and running multiple copies in parallel.
Statistically it can be nearly as good to do the experiment where we change A and all other influences apart from are at least uncorrelated with A, which is more usually what we do — a randomised controlled trial.
In many circumstances though, (budget restrictions, ethical constraints, bad experimental design…) we cannot do these ideal experiments, and a mathematical crutch is needed to get us the next-best outcome, which is to control for the things that we *must* (and not control for the things we must not).

In classic-flavoured causal inference, we use
graphical models
with the additional assumption that \(A\rightarrow B\) may be read as “A causes a change in B”.
This is what you end up with if you use a Structural Equation Model (a.k.a. hierarchical models) to impose a causal structure on the observations.
The result is a particular type of graph, a Directed Acyclic Graph_ (DAG) which, informally put, summarises what can possibly affect what in the model.
Slightly more formally, it summarises what *cannot* (conditionally) affect what.
C&C conditional treatment effect estimation by potential outcomes.

With this tool in hand I can answer the question of when I can use my crappy observational data, collected without a good experimental design for whatever reason, to do interventional inference? There is a lot of research in this area; I should summarise the salient bits for myself.

## What can go wrong?

What can I *actually* identify?
For a start, if we are resorting to this more difficult methodology that *already* suggests that we might be trying to use data which was collected with no regard to our actual statistical needs, and thus we might really stretch to imagine that we can actually find actual appropriate instruments in the data.
Here is an essay on that theme.

OMFG Exogenous Variation! Or, Can You Find Good Nails When You Find an Indonesian Politics Hammer quotes Angus Deaton

we have at least some control over the light but choose to let it fall where it may and then proclaim that whatever it illuminates is what we were looking for all along

## Teaching

Yanir Seroussi’s Causal inference resources recommends

Causal Diagrams: Draw Your Assumptions Before Your Conclusions. A high-level introduction to causal diagrams by Miguel Hernán. Highly recommended for those who want to get a conceptual overview of how causal diagrams work and why they’re useful.A/B Testing by Google: Online Experiment Design and Analysis. Experimentation is key to causal inference, with the online world offering an accessible ground for running experiments. This short course is worth doing if you’re involved in online experiments in any way.

Miguel Hernán and Jamie Robins’ causal inference book (Miguel A. Hernán and Robins 2020) is available in free draft form online. See Yanir Seroussi’s review.

Jonas Peters’ notes from his teaching in 2015 (I think I took this course).

- An Introduction to Bayesian Network Theory and Usage
- pgmpy_notebook/2. Bayesian Networks.ipynb at master · pgmpy/pgmpy_notebook
- cs228 notes

Samantha Kleinberg wrote two classes, introductory and advanced. The latter is notable for handling for time-dependent causality.

Tutorial: David Sontag and Uri Shalit, Causal inference from observational studies. Mastering Metrics: The Path from Cause to Effect A resource list for causality in statistics, data science and physics.

Brady Neal’s Introduction to Causal Inference includes his draft textbook.

Felix Elwert’s summary. (Elwert 2013)

Chapter 3 of (some edition of) Pearl’s book is available as an author’s preprint: Part 1, 2, 3, 4, 5, 6.

Stanford encyclopaedia of philosophy entry.

Various classic introductions (Pearl 2012, 1998; Elwert 2013; Morgan and Winship 2015; Rohrer 2018). Notably not recommended as a pedagogic experience (Koller and Friedman 2009) (although as a reference text it is great and will make you smarter).

The dagitty intro is an interactive guide via visualizations.
Likewise, the ggdag bias structure vignette
shows of the useful explanation diagrams available in `ggdag`

and is also a good introduction to selection bias and causal DAGs themselves.

Amit Sharma’s tutorial at KDD. See also Emily Riederer’s Causal design patterns for data analysts Spurious correlation induced by sampling bias.

Still confused? Overwhelmed? I am. How about a diagram?

## Instrumental variables

## References

*Statistical Methods in Medical Research*25 (5): 2294–314.

*PMLR*.

*Physical Review X*7 (3): 031021.

*arXiv:1703.04025 [Cs, Stat]*, March.

*Proceedings of the National Academy of Sciences*106 (51): 21544–49.

*Conditional Specification of Statistical Models*. Springer Science & Business Media.

*arXiv:1902.07409 [Stat]*, February.

*arXiv:1702.02604 [Cs, Stat]*, February.

*Proceedings of the National Academy of Sciences*113 (27): 7345–52.

*AAAI*, 2410–16.

*arXiv:1812.03253 [Cs, Stat]*.

*Uncertainty in Artificial Intelligence*, 585–94. PMLR.

*arXiv:1507.03652 [Math, Stat]*, July.

*Proceedings of the 27th ACM International Conference on Information and Knowledge Management*, 1003–12. CIKM ’18. New York, NY, USA: ACM.

*arXiv:1611.06221 [Cs, Stat]*, October.

*arXiv:1803.08784 [Cs, Stat]*, March.

*arXiv:1611.06221 [Cs, Stat]*, November.

*arXiv:1209.2355 [Cs, Math, Stat]*, July.

*Scientific Reports*6 (1): 27538.

*Philosophy of Science*83 (1): 60–81.

*Structural Equation Modeling: A Multidisciplinary Journal*9 (4): 459–74.

*arXiv:1301.0560 [Cs]*, December.

*The Annals of Applied Statistics*9 (1): 247–74.

*Mathematical Methods of Operations Research*77 (3): 357–70.

*Statistical Science*35 (3): 404–26.

*Annual Review of Statistics and Its Application*1 (1): 255–78.

*Statistical Methods in Medical Research*22 (5): 466–92.

*Neural Computation*24 (7): 1611–68.

*Physical Review Letters*120 (19): 190401.

*arXiv:1411.1557 [Stat]*, November.

*The Annals of Statistics*40 (1): 294–321.

*Journal of Causal Inference*9 (1): 39–77.

*Biometrika*, October, asr041.

*NIPS Causality: Objectives and Assessment*, 177–90.

*Granger-Causality Graphs for Multivariate Time Series*.

*Handbook of Causal Analysis for Social Research*, edited by Stephen L. Morgan, 245–73. Handbooks of Sociology and Social Research. Dordrecht: Springer Netherlands.

*Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics*, 256–64.

*arXiv:1405.1868 [Stat]*, May.

*arXiv:2104.04103 [Cs, Stat]*, September.

*Games for the superintelligent*. London: Muller.

*The Astrophysical Journal*806 (2): 215.

*Journal of the American Statistical Association*108 (501): 288–300.

*Synthese*197 (4): 1467–86.

*American Journal of Sociology*117 (3): 955–66.

*Applied Bayesian Modeling and Causal Inference From Incomplete-Data Perspectives*. John Wiley & Sons.

*arXiv:2010.12237 [Cs]*, October.

*Annual Review of Statistics and Its Application*6 (1): 103–24.

*Philosophy of Science*65 (1): 1–32.

*arXiv:1403.2310 [Stat]*, March.

*Electronic Journal of Probability*19.

*Annals of Epidemiology*26 (10): 674–80.

*American Journal of Public Health*108 (5): 616–19.

*Causal Inference: What If*.

*Causal Inference Vol 3*.

*Causal Inference Vol 2*.

*Causal Inference Vol 1*.

*Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics*, 128–35. Citeseer.

*Advances in Neural Information Processing Systems 21*, edited by D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, 689–96. Curran Associates, Inc.

*arXiv:2012.08154 [Cs, Stat]*, December.

*The Annals of Statistics*49 (3): 1460–88.

*Artificial Intelligence*182-183 (May): 1–31.

*IEEE Transactions on Information Theory*56 (10): 5168–94.

*arXiv:1605.03661 [Cs, Stat]*, June.

*International Conference on Machine Learning*, 3020–29. PMLR.

*Learning in Graphical Models*. Cambridge, Mass.: MIT Press.

*The Handbook of Brain Theory and Neural Networks*, 490–96.

*Handbook of Neural Networks and Brain Theory*.

*Journal of Machine Learning Research*21 (37): 1–5.

*Journal of Machine Learning Research*8 (May): 613–36.

*Journal of Machine Learning Research*21 (62): 1–54.

*arXiv Preprint arXiv:1510.04740*.

*Advances in Neural Information Processing Systems 30*, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, 656–66. Curran Associates, Inc.

*IJCAI*, 83:190–93. San Francisco, CA, USA: Citeseer.

*Causality, Probability, and Time*. 1 edition. Cambridge: Cambridge University Press.

*Why: A Guide to Finding and Using Causes*. 1st edition. Beijing ; Boston: O’Reilly Media.

*arXiv:1709.02023 [Cs, Math, Stat]*, September.

*Trustworthy Online Controlled Experiments: A Practical Guide to A/B Testing*. 1st edition. Cambridge, United Kingdom ; New York, NY: Cambridge University Press.

*Annual Review of Statistics and Its Application*6 (1): 149–72.

*Probabilistic Graphical Models : Principles and Techniques*. Cambridge, MA: MIT Press.

*Proceedings of the National Academy of Sciences*116 (10): 4156–65.

*Journal of the Royal Statistical Society. Series B (Methodological)*50 (2): 157–224.

*Graphical Models*. Oxford Statistical Science Series. Clarendon Press.

*Complex Stochastic Systems*, 63–107. CRC Press.

*arXiv:1811.12359 [Cs, Stat]*, June.

*arXiv:1605.08179 [Cs, Stat]*, May.

*Advances in Neural Information Processing Systems 30*, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, 6446–56. Curran Associates, Inc.

*arXiv Preprint arXiv:1307.5636*.

*Nature Methods*7 (4): 247–48.

*The Annals of Statistics*37 (6A): 3133–64.

*arXiv:1903.03662 [Stat]*, March.

*Proceedings of the National Academy of Sciences*107 (14): 6286–91.

*2018 IEEE Data Science Workshop (DSW)*, 6–10.

*New England Journal of Medicine*367 (16): 1562–64.

*Proceedings of the 24th International Conference on Machine Learning*, 625–32. ACM.

*UAI2018*, 17.

*Journal of Machine Learning Research*17 (32): 1–102.

*Counterfactuals and Causal Inference*. Cambridge University Press.

*Cancer Investigation*40 (7): 1–10.

*Machine learning: a probabilistic perspective*. 1 edition. Adaptive computation and machine learning series. Cambridge, MA: MIT Press.

*arXiv:1911.06030 [Stat]*, November.

*Course Lecture Notes (Draft)*.

*Learning Bayesian Networks*. Vol. 38. Prentice Hal, Paperback.

*arXiv:1910.08527 [Cs, Stat]*, February.

*Advances In Neural Information Processing Systems*.

*International Journal of Epidemiology*50 (2): 613–19.

*Social Networks*33 (3): 211–18.

*arXiv:2110.10819 [Cs]*, October.

*Proceedings of the Second AAAI Conference on Artificial Intelligence*, 133–36. AAAI’82. Pittsburgh, Pennsylvania: AAAI Press.

*Artificial Intelligence*29 (3): 241–88.

*Quantified Representation of Uncertainty and Imprecision*, edited by Philippe Smets, 367–89. Handbook of Defeasible Reasoning and Uncertainty Management Systems. Dordrecht: Springer Netherlands.

*Probabilistic reasoning in intelligent systems: networks of plausible inference*. Rev. 2. print., 12. [Dr.]. The Morgan Kaufmann series in representation and reasoning. San Francisco, Calif: Kaufmann.

*Statistics Surveys*3: 96–146.

*Causality: Models, Reasoning and Inference*. Cambridge University Press.

*Sociological Methodology*40 (1): 75–149.

*Statistical Science*29 (4): 579–95.

*Causal Inference in Statistics: A Primer*. Wiley.

*arXiv:1501.01332 [Stat]*, January.

*Elements of Causal Inference: Foundations and Learning Algorithms*. Adaptive Computation and Machine Learning Series. Cambridge, Massachuestts: The MIT Press.

*The Journal of Machine Learning Research*15 (1): 2009–53.

*2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)*, 958–65.

*Proceedings of the 27th ACM International Conference on Information and Knowledge Management*, 1679–82. CIKM ’18. New York, NY, USA: Association for Computing Machinery.

*Current Epidemiology Reports*3 (1): 63–71.

*Annals of Statistics*30 (4): 962–1030.

*Latent Variable Modeling and Applications to Causality*, edited by Maia Berkane, 69–117. Lecture Notes in Statistics. New York, NY: Springer.

*Advances in Methods and Practices in Psychological Science*, January.

*arXiv:1801.06229 [Stat]*, May.

*Journal of Machine Learning Research*21 (188): 1–86.

*Uncertainty in Artificial Intelligence*.

*arXiv:1707.00819 [Cs, Stat]*, July.

*Statistical Science*21 (2): 206–22.

*Use of Directed Acyclic Graphs*. Agency for Healthcare Research and Quality (US).

*Probabilistic and Causal Inference: The Works of Judea Pearl*, 1st ed., 36:765–804. New York, NY, USA: Association for Computing Machinery.

*arXiv:1505.03036 [Astro-Ph, Stat]*, May.

*ICML 2012*.

*Proceedings of the IEEE*109 (5): 612–34.

*arXiv:1501.06794 [Cs, Stat]*, January.

*Proceedings of the 31st International Conference on Neural Information Processing Systems*, 1696–706. NIPS’17. Red Hook, NY, USA: Curran Associates Inc.

*arXiv:1607.06565 [Physics, Stat]*, July.

*Sociological Methods & Research*40 (2): 211–39.

*Cause and Correlation in Biology: A User’s Guide to Path Analysis, Structural Equations and Causal Inference with R*. 2nd ed. Cambridge: Cambridge University Press.

*The Journal of Machine Learning Research*9: 1941–79.

*arXiv:1411.2127 [Stat]*, November.

*BMC Medical Research Methodology*8 (1): 70.

*arXiv:2007.04511 [Stat]*, July.

*Proceedings of the Conference on Empirical Methods in Natural Language Processing*, 145–56. Association for Computational Linguistics.

*Causation, Prediction, and Search*. Second Edition. Adaptive Computation and Machine Learning. The MIT Press.

*The 22nd International Conference on Artificial Intelligence and Statistics*, 3118–27. PMLR.

*Journal of Epidemiology*30 (4): 153–62.

*arXiv:1508.00280 [Cs]*, August.

*Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence*, 681–88. UAI’11. Arlington, Virginia, USA: AUAI Press.

*arXiv:1710.05899 [Cs]*, July.

*arXiv:1807.04010 [Cs, Stat]*, July.

*Statistical Methods in Medical Research*21 (1): 7–30.

*arXiv:1407.2483 [Cs, Stat]*, July.

*Evolution*68 (7): 2128–36.

*arXiv:1710.02428 [Astro-Ph]*, October.

*arXiv:2002.06060 [q-Bio, Stat]*, July.

*PLOS ONE*11 (3): e0152719.

*arXiv:2007.10979 [Cs, Stat]*, July.

*The Annals of Mathematical Statistics*5 (3): 161–215.

*arXiv:1611.04660 [Cs, Stat]*, November.

*arXiv:2004.08697 [Cs, Stat]*, July.

*Exploring Artificial Intelligence in the New Millennium*, edited by G. Lakemeyer and B. Nebel, 239–36. Morgan Kaufmann Publishers.

*Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence*, 3315–21. AAAI’16. Phoenix, Arizona: AAAI Press.

*Proceedings of the UAI 2014 Conference on Causal Inference: Learning and Prediction - Volume 1274*, 11–24. CI’14. Aachen, DEU: CEUR-WS.org.

*Proceedings of the 24th International Conference on Artificial Intelligence*, 3243–49. IJCAI’15. Buenos Aires, Argentina: AAAI Press.

*arXiv:1202.3775 [Cs, Stat]*, February.

*Advances in Neural Information Processing Systems 31*, edited by S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, 31:9472–83. Curran Associates, Inc.

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