1. What is the expected value of the demand Q if the price is reported to be P = p0?
2. What is the expected value of the demand Q if the price is set to P = p0?
3. Given that the current price is P = p0, what would the expected value of the demand Q be if we were to set the price at P = p1?
The reader should recognize these queries as coming from the three levels of the Ladder of Causation: predictions, actions, and counterfactuals. As I expected, respondents had no trouble answering question 1, one person (a distinguished professor) was able to solve question 2, and nobody managed to answer question 3.
The Model Penal Code expresses: This is a set of standard legal principles proposed by the American Law Institute in 1962 to bring uniformity to the various state legal codes. It does not have full legal force in any state, but according to Wikipedia, as of 2016, more than two-thirds of the states have enacted parts of the Model Penal Code.
Заметки к главе девятой
Those sailors who had eaten: The reason is that polar bear livers do contain vitamin C.
“On the Inadequacy of the Partial”: The title refers to partial correlation, a standard method of controlling for a confounder that we discussed in Chapter 7.
Here is how to define the NIE: In the original delivery room, NIE was expressed using nested subscripts, as in Y(0,M). I hope the reader will find the mixture of counterfactual subscripts and do-operators above more transparent.
In that year researchers identified: To be technically correct it should be called a “single nucleotide polymorphism,” or SNP. It is a single letter in the genetic code, while a gene is more like a word or a sentence. However, in order not to burden the reader with unfamiliar terminology, I will simply refer to it as a gene.
Библиография
Введение: ум важнее данных
Annotated Bibliography
The history of probability and statistics from antiquity to modern days is covered in depth by Hacking (1990); Stigler (1986, 1999, 2016). A less technical account is given in Salsburg (2002). Comprehensive accounts of the history of causal thought are unfortunately lacking, though interesting material can be found in Hoover (2008); Kleinberg (2015); Losee (2012); Mumford and Anjum (2014). The prohibition on causal talk can be seen in almost every standard statistical text, for example, Freedman, Pisani, and Purves (2007) or Efron and Hastie (2016). For an analysis of this prohibition as a linguistic impediment, see Pearl (2009, Chapters 5 and 11), and as a cultural barrier, see Pearl (2000b). Recent accounts of the achievements and limitations of Big Data and machine learning are Darwiche (2017); Pearl (2017); Mayer-Schönberger and Cukier (2013); Domingos (2015); Marcus (July 30, 2017). Toulmin (1961) provides historical context to this debate. Readers interested in “model discovery” and more technical treatments of the do-operator can consult Pearl (1994, 2000a, Chapters 2–3); Spirtes, Glymour, and Scheines (2000). For a gentler introduction, see Pearl, Glymour, and Jewell (2016). This last source is recommended for readers with college-level mathematical skills but no background in statistics or computer science. It also provides basic introduction to conditional probabilities, Bayes’s rule, regression, and graphs.
Earlier versions of the inference engine shown in Figure 1.1 can be found in Pearl (2012); Pearl and Bareinboim (2014).
References
Darwiche, A. (2017). Human-level intelligence or animal-like abilities? Tech. rep., Department of Computer Science, University of California, Los Angeles, CA. Submitted to Communications of the ACM. Accessed online at https://arXiv:1707.04327.
Domingos, P. (2015). The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World. Basic Books, New York, NY.
Efron, B., and Hastie, T. (2016). Computer Age Statistical Inference. Cambridge University Press, New York, NY.
Freedman, D., Pisani, R., and Purves, R. (2007). Statistics. 4th ed. W. W. Norton & Company, New York, NY.
Hacking, I. (1990). The Taming of Chance (Ideas in Context). Cambridge University Press, Cambridge, UK.
Hoover, K. (2008). Causality in economics and econometrics. In The New Palgrave Dictionary of Economics (S. Durlauf and L. Blume, eds.), 2nd ed. Palgrave Macmillan, New York, NY.
Kleinberg, S. (2015). Why: A Guide to Finding and Using Causes. O’Reilly Media, Sebastopol, CA.
Losee, J. (2012). Theories of Causality: From Antiquity to the Present. Routledge, New York, NY.
Marcus, G. (July 30, 2017). Artificial intelligence is stuck. Here’s how to move it forward. New York Times, SR6.
Mayer-Schönberger, V., and Cukier, K. (2013). Big Data: A Revolution That Will Transform How We Live, Work, and Think. Houghton Mifflin Harcourt Publishing, New York, NY.
Morgan, S., and Winship, C. (2015). Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research). 2nd ed. Cambridge University Press, New York, NY.
Mumford, S., and Anjum, R. L. (2014). Causation: A Very Short Introduction (Very Short Introductions). Oxford University Press, New York, NY.
Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo, CA.
Pearl, J. (1994). A probabilistic calculus of actions. In Uncertainty in Artificial Intelligence 10 (R. L. de Mantaras and D. Poole, eds.). Morgan Kaufmann, San Mateo, CA, 454–462.
Pearl, J. (1995). Causal diagrams for empirical research. Biometrika 82: 669–710.
Pearl, J. (2000a). Causality: Models, Reasoning, and Inference. Cambridge University Press, New York, NY.
Pearl, J. (2000b). Comment on A. P. Dawid’s Causal inference without counterfactuals. Journal of the American Statistical Association 95: 428–431.
Pearl, J. (2009). Causality: Models, Reasoning, and Inference. 2nd ed. Cambridge University Press, New York, NY.
Pearl, J. (2012). The causal foundations of structural equation modeling. In Handbook of Structural Equation Modeling (R. Hoyle, ed.). Guilford Press, New York, NY, 68–91.
Pearl, J. (2017). Advances in deep neural networks, at ACM Turing 5 °Celebration. Available at: https://www.youtube.com/watch?v=mFYM9j8bGtg (June 23, 2017).
Pearl, J., and Bareinboim, E. (2014). External validity: From do-calculus to transportability across populations. Statistical Science 29:579–595.
Pearl, J., Glymour, M., and Jewell, N. (2016). Causal Inference in Statistics: A Primer. Wiley, New York, NY.
