by Nate Silver
65. Per NewsLibrary.com. In figure 7-4, figures for articles discussing autism are adjusted to reflect the overall volume of articles in the NewsLibrary.com database in a given year, and then indexed so as to be on the same scale as the number of public schoolchildren receiving special education programs for autism under the IDEAS Act.
66. Tomohisa Yamashita, Kiyoshi Izumi, Koichi Kurumatani, “Effective Information Sharing Based on Mass User Support for Reduction of Traffic Congestion,” presented at the New England Complex Systems Institute’s Fifth International Conference on Complex Systems, May 16–21, 2004. http://www.necsi.edu/events/iccs/openconf/author/papers/f190.pdf.
67. Hyejin Youn, Hawoong Jeong, and Michael T. Gastner, “The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control,” Physical Review Letters, 101, August 2008. http://arxiv.org/pdf/0712.1598.pdf.
68. Hanna Kokko, “Useful Ways of Being Wrong,” Journal of Evolutionary Biology, 18 (2005), pp. 1155–1157. http://www.anu.edu.au/BoZo/kokko/Publ/Wrong.pdf.
69. W. O. Kermack and A. G. McKendrick, “A Contribution to the Mathematical Theory of Epidemics,” Proceedings of the Royal Society A, 115 (1927), pp. 700–721.
70. H-H. M. Truong, et al., “Increases in Sexually Transmitted Infections and Sexual Risk Behaviour Without a Concurrent Increase in HIV Incidence Among Men Who Have Sex with Men in San Francisco: A Suggestion of HIV Serosorting?,” Sexually Transmitted Infections, 82, 6 (2006), pp. 461–466.
71. “Condom fatigue” is the idea that gay men had simply grown sick and tired of being told that they needed to use a condom every time they had sex.
72. Thomas H. Maugh II, “Experts Fear Resurgence of HIV Infection,” Los Angeles Times, July 8, 2000. http://articles.latimes.com/2000/jul/08/news/mn-49552.
73. MSM is the preferred term in the medical literature in this context; it is more precise than terms like homosexual and particularly gay, which often refer to sexual identity rather than sexual behavior. Some men who identify as straight (or bisexual) nevertheless have sex with other men; and some men who identify as gay may nevertheless have sex with women, or may be celibate.
74. San Francisco Department of Public Health.
75. Christopher S. Hall and Gail Bolan, “Syphilis and HIV,” HIV InSite Knowledge Base Chapter, University of California San Francisco; June 2006. http://hivinsite.ucsf.edu/InSite?page=kb-05-01-04.
76. H-H M. Truong et al., “Increases in Sexually Transmitted Infections and Sexual Risk Behaviour Without a Concurrent Increase in HIV Incidence Among Men Who Have Sex with Men in San Francisco: A Suggestion of HIV Serosorting?”
77. Fengyi Jin, et al., “Per-Contact Probability of HIV Transmission in Homosexual Men in Sydney in the Era of HAART,” AIDS, 24, pp. 907–913, 2010. http://www.who.int/hiv/events/artprevention/jin_per.pdf.
78. Much of the research suggested that it was HIV-positive men who were driving the trend: most HIV-positive men would much prefer to have sex with other HIV-positive partners, particularly if they are not planning to use a condom. The advent of the Internet, as well as various types of support networks in the offline world, has made that much easier to do.
79. Larry Green, “Measles on Rise Nationwide; Chicago Worst Hit,” Los Angeles Times, August 5, 1989. http://articles.latimes.com/1989-08-05/news/mn-469_1_chicago-health.
80. Justin Lessler et al., “Transmissibility of Swine Flu at Fort Dix, 1976,” Journal of the Royal Society Interface, 4, no. 15, pp. 755–762, August 2007. http://rsif.royalsocietypublishing.org/content/4/15/755.full.
81. Ibid.
82. “Keep it sophisticatedly simple” was a phrase used by the late economist Arnold Zellner.
83. “Healthy Hand Washing Survey 2011,” Bradley Corp. http://www.bradleycorp.com/handwashing/survey.jsp.
84. http://www.altpenis.com/penis_news/20060710032108data_trunc_sys.shtml.
85. “An Agent-Based Approach to HIV/AIDS Epidemic Modeling: A Case Study of Papua New Guinea, thesis, Massachusetts Institute of Technology, 2006. http://dspace.mit.edu/handle/1721.1/34528.
86. Shan Mei, et al., “Complex Agent Networks Explaining the HIV Epidemic Among Homosexual Men in Amsterdam,” Mathematics and Computers in Simulation, 80, no. 5, January 2010. http://portal.acm.org/citation.cfm?id=1743988.
87. Donald G. McNeil Jr., “Predicting Flu with the Aid of (George) Washington,” New York Times, May 3, 2009. http://www.nytimes.com/2009/05/04/health/04model.html?hp.
88. Michael A. Babyak, “What You See May Not Be What You Get: A Brief, Nontechnical Introduction to Overfitting in Regression-Type Models,” Statistical Corner, Psychosomatic Medicine, 66 (2004), pp. 411–421.
89. Even if a prediction model is just a sort of thought experiment that is years away from producing useful results, it can still help us understand the scope of a problem. The Drake equation, a formula that provides a framework for predicting the number of intelligent extraterrestrial species in the galaxy, is not likely to yield highly useful and verifiable predictions in the span of our lifetimes—nor, probably, in the span of human civilization. The uncertainties are too great. Too many of its parameters are not known to within an order of magnitude; depending on which values you plug in, it can yield answers anywhere from that we are all alone in the universe to that there are billions and billions of extraterrestrial species. However, the Drake equation has nevertheless been a highly useful lens for astronomers to think about life, the universe, and everything.
90. George E. P. Box and Norman R. Draper, Empirical Model-Building and Response Surfaces (New York: Wiley, 1987), p. 424.
91. “Norbert Wiener,” Wikiquote.org. http://en.wikiquote.org/wiki/Norbert_Wiener.
CHAPTER 8: LESS AND LESS AND LESS WRONG
1. Roland Lazenby, The Show: The Inside Story of the Spectacular Los Angeles Lakers in the Words of Those Who Lived It (New York: McGraw-Hill Professional, 2006).
2. Mark Heisler, “The Times’ Rankings: Top to Bottom/NBA,” Los Angeles Times, November 7, 1999.
3. Tom Spousta, “Pro Basketball: Trail Blazers Have Had Some Success Containing O’Neal,” New York Times, May 20, 2000. http://www.nytimes.com/2000/05/20/sports/pro-basketball-trail-blazers-have-had-some-success-containing-o-neal.html?scp=2&sq=lakers+portland&st=nyt.
4. “Blazer Blowout Shows Need for ‘Sheed,” Associated Press; May 22, 2000. http://web.archive.org/web/20041226093339/http://sportsmed.starwave.com/nba/2000/20000522/recap/porlal.html.
5. Tom Spousta, “Pro Basketball: Game 2 Was a Blur as Lakers Lost Focus,” New York Times, May 24, 2000. http://www.nytimes.com/2000/05/24/sports/pro-basketball-game-2-was-a-blur-as-lakers-lost-focus.html?scp=3&sq=lakers+portland&st=nyt.
6. Tom Spousta, “Pro Basketball: Lakers Rally and Get Back on Track,” New York Times, May 27, 2012. http://www.nytimes.com/2000/05/27/sports/pro-basketball-lakers-rally-and-get-back-on-track.html?scp=14&sq=lakers+portland&st=nyt.
7. Tom Spousta, “Pro Basketball: Everything Comes Up Roses for the Lakers,” New York Times, May 29, 2000. http://www.nytimes.com/2000/05/29/sports/pro-basketball-everything-comes-up-roses-for-the-lakers.html?scp=16&sq=lakers+portland&st=nyt.
8. “Seventh Heaven: Blazers Send Series Back to L.A. for Game 7,” Associated Press via Sports Illustrated, June 3, 2000. http://sportsillustrated.cnn.com/basketball/nba/2000/playoffs/news/2000/06/02/lakers_blazers_gm6_ap/.
9. That is, $300,000 from winning his $200,000 bet on Portland at 3-to-2 odds, less the $80,000 that Voulgaris originally bet on the Lakers.
10. Tom Spousta, “Pro Basketball: Trail Blazers Follow Plan to the Bitter End,” New York Times, June 7, 2000. http://www.nytimes.com/2000/06/05/sports/pro-basketball-trail-blazers-follow-plan-to-the-bitter-end.html?scp=28&sq=lakers+portland&st=nyt.
11. Per play-by-play data downloaded from Basketballvalue.com. http://basketballvalue.com/downloads.php.
12. This is based on a logistic regression analysis I conducted of all games played in the 2009–2010 NBA regular season, where the independent varia
ble is the score margin between the home team and the away team with fourteen minutes left to play in the game, and the dependent variable is whether or not the home team ultimately won. The regression model yields a value of .056 when the scoring margin is –16; that is, the home team has a 5.6 percent chance of victory when trailing by sixteen points, which translates into odds 17-to-1 against. I round down slightly to 15 to 1 because a team trailing by sixteen points at home will usually be inferior to its opponent, whereas the Lakers and Blazers were more evenly matched.
13. Voulgaris’s odds of winning his bet at the start of the evening were about 50 percent: a 60 percent chance that the Lakers beat the Blazers in Game 7 multiplied by what I’ve estimated to be an 83 percent chance that the Lakers would beat the Pacers if advancing to the final. By that point in the game, the Lakers’ odds of winning the Championship were down to about 5 percent: a 6 percent chance of coming back to beat the Blazers, multiplied by an 83 percent chance of beating the Pacers.
14. Miranda Hitti, “Testosterone Ups Home Field Advantage,” WebMD Health News, June 21, 2006. http://www.webmd.com/fitness-exercise/news/20060621/testosterone-ups-home-field-advantage.
15. Most sports leagues hold their drafts in reverse order of finish: the team with the worst record is the first to pick. In the NBA, a sport where a single superstar talent can make an exceptional amount of difference, the league holds a draft lottery so as to discourage teams from tanking their games at the end of the season to improve their drafting position. Nevertheless, the worse a team does, the more Ping-Pong balls it gets in the lottery, and so teams will often play something other than their best basketball in these scenarios.
16. This asymmetry would not exist to the same extent if basketball teams were more focused on individual defensive statistics. But offense is relatively easy to measure, and defense is relatively hard; some teams don’t even try to measure individual defensive performance at all. A player who scores a basket will therefore gain more market value than the man defending will lose by conceding one.
17. “2001–02 Cleveland Cavaliers Schedule and Results,” Basketball-Reference.com. http://www.basketball-reference.com/teams/CLE/2002_games.html.
18. On average, a team will go either over or under the total five games in a row about five times per season. That works out to 150 such streaks per season between the thirty NBA teams combined.
19. D. R. Bellhouse, “The Reverend Thomas Bayes FRS: A Biography to Celebrate the Tercentenary of His Birth,” Statistical Science, 19, 1, pp. 3–43; 2004. http://www2.isye.gatech.edu/~brani/isyebayes/bank/bayesbiog.pdf.
20. Bayes may also have been an Arian, meaning someone who followed the teachings of the early Christian leader Arias and who regarded Jesus Christ as the divine son of God rather than (as most Christians then and now believe) a direct manifestation of God.
21. Thomas Bayes, “Divine Benevolence: Or an Attempt to Prove That the Principal End of the Divine Providence and Government Is the Happiness of His Creatures.” http://archive.org/details/DivineBenevolenceOrAnAttemptToProveThatThe.
22. Ibid.
23. Ibid.
24. The Late Rev. Mr. Bayes, Communicated by Mr. Price, in a Letter to John Canton, M. A. and F. R. S., “An Essay Towards Solving a Problem in the Doctrine of Chances,” Philosophical Transactions of the Royal Society of London, 53, pp. 370–418; 1763. http://www.stat.ucla.edu/history/essay.pdf.
25. Donald A. Gillies, “Was Bayes a Bayesian?,” Historia Mathematica, 14, no. 4, pp. 325–346, November 1987. http://www.sciencedirect.com/science/article/pii/0315086087900656.
26. David Hume, “Cause and Effect” in An Enquiry Concerning Human Understanding (1772) (Hackett Publishing Company, 1993). http://www.marxists.org/reference/subject/philosophy/works/en/hume.htm.
27. Some Christians regard Bayesian probability as more compatible with their worldview. Under Bayes’s theorem, if you assign a 100 percent prior probability to the hypothesis that a Christian God exists, then no amount of worldly evidence will shake you from that conviction. It is plausible that Bayes was aware of this property; in introducing Bayes’s essay, Richard Price mentioned that he thought Bayes’s theorem helped to confirm “the existence of the Diety.”
For further discussion, see Steve Bishop, “Christian Mathematicians—Bayes, God & Math: Thinking Christianly About Mathematics,” Education, March 22, 2012. http://godandmath.com/2012/03/22/christian-mathematicians-bayes/.
28. “Fundamental Atheism,” Free Atheist Church. https://sites.google.com/site/freeatheistchurch/fundamental-atheism.
29. Sharon Bertsch McGrayne, The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy (New Haven, CT: Yale University Press, Kindle edition), 427–436.
30. E. O. Lovett, “The Great Inequality of Jupiter and Saturn,” Astronomical Journal, 15, 351 (1895), pp. 113–127.
31. McGrayne, The Theory That Would Not Die, Kindle location 19.
32. Pierre-Simon Laplace, “A Philosophical Essay on Probabilities” (1902), pp. 6–8.
33. Bret Schulte, “How Common Are Cheating Spouses?” U.S. News & World Report, March 27, 2008. http://www.usnews.com/news/national/articles/2008/03/27/how-common-are-cheating-spouses.
34. “Breast Cancer Risk by Age,” Breast Cancer Centers for Disease Control and Prevention, last updated August 13, 2010. http://www.cdc.gov/cancer/breast/statistics/age.htm.
35. “Understanding Breast Exam Results—False Negative–False Positive Results,” RealAge.com. http://www.realage.com/womens-health/breast-exam-results.
36. S. Eva Singletary, Geoffrey L. Robb, and Gabriel N. Hortobagyi, “Advanced Therapy of Breast Disease,” B. C. Decker, May 30, 2004.
37. Gina Kolata, “Panel Urges Mammograms at 50, Not 40,” New York Times, November 16, 2009. http://www.nytimes.com/2009/11/17/health/17cancer.html.
38. Dan M. Kahan, et al., “The Polarizing Impact of Science Literacy and Numeracy on Perceived Climate Change Risks,” Nature Climate Change, May 27, 2012. See Supplementary Information: http://www.nature.com/nclimate/journal/vaop/ncurrent/extref/nclimate1547-s1.pdf.
39. Twenty-five thousand days prior to September 11, 2001, would take us back to 1942.
40. John P. A. Ioannidis, “Why Most Published Research Findings Are False,” PLOS Medicine, 2, e124, August 2005. http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124.
41. Brian Owens, “Reliability of ‘New Drug Target’ Claims Called into Question,” NewsBlog, Nature, September 5, 2011. http://blogs.nature.com/news/2011/09/reliability_of_new_drug_target.html.
42. McGrayne, The Theory That Would Not Die, Kindle location 46.
43. Paul D. Stolley, “When Genius Errs: R. A. Fisher and the Lung Cancer Controversy,” American Journal of Epidemiology, 133, 5, 1991. http://www.epidemiology.ch/history/PDF%20bg/Stolley%20PD%201991%20when%20genius%20errs%20-%20RA%20fisher%20and%20the%20lung%20cancer.pdf.
44. Alan Agresti and David B. Hitchcock, “Bayesian Inference for Categorical Data Analysis,” Statistical Methods & Applications, 14 (2005), pp. 297–330. http://www.stat.ufl.edu/~aa/articles/agresti_hitchcock_2005.pdf.
45. John Aldrich, “R. A. Fisher on Bayes and Bayes’ Theorem,” Bayesian Analysis, 3, no. 1 (2008), pp. 161–170. http://ba.stat.cmu.edu/journal/2008/vol03/issue01/aldrich.pdf.
46. McGrayne, The Theory That Would Not Die, Kindle location 48.
47. Tore Schweder, “Fisherian or Bayesian Methods of Integrating Diverse Statistical Information?” Fisheries Research, 37, 1–3 (August 1998), pp. 61–75. http://www.sciencedirect.com/science/article/pii/S0165783698001271.
48. 2008 New Hampshire Democratic Primary polls via RealClearPolitics.com. http://www.realclearpolitics.com/epolls/2008/president/nh/new_hampshire_democratic_primary-194.html.
49. Nate Silver, “Rasmussen Polls Were Biased and Inaccurate; Quinnipiac, SurveyUSA Performed Strongly,” FiveThirtyEight, New York Times, November
4, 2010. http://fivethirtyeight.blogs.nytimes.com/2010/11/04/rasmussen-polls-were-biased-and-inaccurate-quinnipiac-surveyusa-performed-strongly/.
50. R. A. Grant and T. Halliday, “Predicting the Unpredictable: Evidence of Pre-Seismic Anticipatory Behaviour in the Common Toad,” Journal of Zoology, 700, January 25, 2010. http://image.guardian.co.uk/sys-files/Environment/documents/2010/03/30/toads.pdf.
51. “Hate Group Formation Associated with Big-Box Stores,” ScienceNewsline.com, April 11, 2012. http://www.sciencenewsline.com/psychology/2012041121000031.html.
52. Aldrich, “R. A. Fisher on Bayes and Bayes’ Theorem.”
53. McGrayne, The Theory That Would Not Die, Kindle location 111.
54. Sir Ronald A. Fisher, “Smoking: The Cancer Controversy,” Oliver and Boyd. http://www.york.ac.uk/depts/maths/histstat/smoking.htm.
55. Jean Marston, “Smoking Gun,” NewScientist, no. 2646, March 8, 2008. http://www.newscientist.com/article/mg19726460.900-smoking-gun.html.
56. McGrayne, The Theory That Would Not Die, Kindle location 113.
57. Stolley, “When Genius Errs.”
58. Ibid.
59. Jo Tuckman and Robert Booth, “Four-Year-Old Could Hold Key in Search for Source of Swine Flu Outbreak,” The Guardian; April 27, 2009. http://www.guardian.co.uk/world/2009/apr/27/swine-flu-search-outbreak-source
60. McGrayne, The Theory That Would Not Die, Kindle location 7.
61. Raymond S. Nickerson, “Null Hypothesis Significance Testing: A Review of an Old and Continuing Controversy,” Psychological Methods, 5, 2 (2000), pp. 241–301. http://203.64.159.11/richman/plogxx/gallery/17/%E9%AB%98%E7%B5%B1%E5%A0%B1%E5%91%8A.pdf.
62. Andrew Gelman and Cosma Tohilla Shalizi, “Philosophy and the Practice of Bayesian Statistics,” British Journal of Mathematical and Statistical Psychology, pp. 1–31, January 11, 2012. http://www.stat.columbia.edu/~gelman/research/published/philosophy.pdf.