The Theory That Would Not Die
Page 34
5. Alastair Denniston in Copeland (2006) 57 and (2004) 219.
6. Patrick Mahon in Copeland (2004) 271.
7. Ibid., 279.
8. Max Newman in Gandy and Yates 7.
9. Copeland (2006) 379.
10. Copeland (2004) 258.
11. Copeland (2006) 379.
12. Copeland (2004) 281.
13. Good (1979) 394.
14. Anonymous to author.
15. Britton 214.
16. Hinsley and Stripp 155.
17. Good interview.
18. Michie’s draft chapter and Good interview.
19. Copeland (2004) 279.
20. Ibid., 287–88.
21. Ibid., 292.
22. Ibid., 289.
23. Ibid., 260.
24. For the entire letter episode, ibid., 336–37.
25. Shiryaev (1991) 313.
26. Ibid.
27. Kolmogorov (1942).
28. Arnold.
29. Copeland (2006) 383.
30. Copeland (2006) 380–82.
31. Turing (1942).
32. Shannon in Kahn (1967) 744.
33. Waddington 27.
34. Koopman (1946) 771.
35. Koopman (1980) 17.
36. Ibid., 18.
37. Ibid., 60–61.
38. Andresen 82–83.
39. Copeland (2006) 80–81.
40. Michie in Copeland (2006) 380.
41. Ibid., 244.
42. Edward H. Simpson letter to author.
43. Ibid.
44. Good in Britton 221.
45. Hodges (2000) 290.
46. Dennis Lindley letter to author.
47. Hilton 7.
5. Dead and Buried Again
1. Good interview.
2. Sampson et al. 135.
3. John W. Pratt interview.
4. Perks 286.
5. DeGroot (1986a) 40–53.
6. Kotz and Johnson I xxxviii.
7. Anonymous in Reid 273.
6. Arthur Bailey
1. Biographical details are from interviews and correspondence with his son and daughter-in-law, Robert A. and Shirley Bailey.
2. Bailey (1942, 1943) 31–32.
3. Hewitt (1969) 80.
4. Bailey (1950) 7.
5. Ibid., 31–32.
6. Ibid., 7–9.
7. Pruitt 165.
8. Bailey (1950) 8.
9. PCAS 37 94–115.
10. The Longley-Cook episode is in Carr 241–43.
11. Charles C. Hewitt Jr. interview.
12. Hans Bühlmann letter to author.
7. From Tool to Theology
1. Stephan et al., 953.
2. Good interview.
3. Reid 216.
4. Fisher (1958) 274.
5. Reid 256.
6. Ibid., 226.
7. Ibid., 274.
8. Good in Kotz and Johnson I 380.
9. Fienberg (2006) 19.
10. Lindley in Smith (1995) 312.
11. Donald Michie in Copeland (2006) 240.
12. Stephen Fienberg interview.
13. George E. P. Box interview.
14. Smith (1995) 308.
15. Sampson (1999) 126–27.
16. Ibid., 128.
17. Kotz and Johnson I 520.
18. Lindley (1989) 14.
19. Savage (1956).
20. Lindley in Erickson 49.
21. Savage in Fienberg (2006) 16–19.
22. Schrödinger 704.
23. Savage in Erickson 297.
24. David Spiegelhalter interview.
25. Robert E. Kass interview.
26. Anonymous.
27. Maurice G. Kendall 185.
28. Kruskal in Brooks, online.
29. Savage in Lindley letter to author.
30. Rivett.
31. Lindley letter to author.
32. Smith (1995) 312.
33. Lindley letter to author.
8. Jerome Cornfield, Lung Cancer, and Heart Attacks
1. Marvin Hoffenberg interview.
2. Ibid.
3. Cornfield (1975) 14.
4. Memorial Symposium 55.
5. Gail 9.
6. Ibid.
7. Gail 10.
8. Stories from Memorial Symposium 52 and 56.
9. Cornfield (1962) 58.
10. Gail 5.
11. Cornfield (1967) 41.
12. Cornfield (1975) 9–11.
13. Memorial Symposium 52.
14. Ellen Cornfield interview.
9. There’s Always a First Time
1. Jardini 119.
2. Harken.
3. Albert Madansky interview.
4. Iklé (1958) 3.
5. Ibid., 73.
6. Ibid., 8, 114.
7. Iklé (1958) 74.
8. Madansky interview.
9. Lindley (1985) 104.
10. Madansky interview.
11. Ibid.
12. Ibid.
13. Iklé (1958) 54.
14. Ibid., 53–54.
15. Madansky interview.
16. Iklé (1958) 153.
17. Iklé (2006) 46–47.
18. Ibid.
19. Ibid.
10. 46,656 Varieties
1. Good (1971) 62–63.
2. Glenn Shafer interview.
3. Lindley letter to author.
4. Box interview.
5. Ibid.
6. Efron (1977) and interview.
7. Box interview.
8. Box (2006) 555–56.
9. Bross (1962) 309–10.
10. Savage (1962) 307.
11. Ericson (1981) 299.
12. Box interview.
13. “What I . . . me . . . it was . . . angry . . . heads.” Lindley to Smith (1995) 310–11.
14. Bennett 36.
15. Smith (1995) 311.
16. Box interview.
17. Ibid.
18. Homer Warner interview.
19. Leahy (1960) 50.
20. Tribe (1971a) 1376.
11. Business Decisions
1. Fienberg (1990) 206.
2. Schleifer interview.
3. Pratt interview.
4. Pratt, Raiffa, Schlaifer (1965) 1.1.
5. Savage (1956) letter.
6. Schlaifer letter of August 22, 1956.
7. Memorial Service (1994).
8. Arthur Schleifer interview.
9. Raiffa in Fienberg (2008) 137.
10. Ibid., 138.
11. Ibid., 139.
12. Ibid., 141.
13. Fienberg (2006) 10.
14. Raiffa (1968) 283.
15. Raiffa interview.
16. Raiffa (2006) 32.
17. Fienberg (2008) 10.
18. Raiffa interview.
19. Memorial Service.
20. Fienberg (2008) 142.
21. Pratt, Memorial Service.
22. Memorial Service.
23. Arthur Schleifer interview.
24. Ibid.
25. Ibid.
26. Fienberg (2006) 18.
27. Raiffa (2006) 48, 51.
28. Raiffa interview.
29. Schleifer interview.
30. Raiffa, Memorial Service.
31. Raiffa (1968).
32. Lindley in Smith (1995) 312.
33. McGinnis.
34. Raiffa and Pratt (1995).
12. Who Wrote The Federalist?
1. Most of the quotations from Mosteller and Wallace in this chapter come from their book, published in 1964 and 1984 under different titles. Exceptions will be noted.
2. David L. Wallace interview.
3. Fienberg et al. 147.
4. Ibid., 192.
5. Petrosino.
6. Kolata 397.
7. DeGroot (1986c) 322.
8. Albers et al. (1990) 256–57.
9. Kolata 398.
10. Robert E. Kass interview.
13. The Cold Warrior
1. Bamford 430–31. The author covered this con
troversy for the Trenton N.J. Times.
2. Stephen Fienberg interview and e-mail.
3. Brillinger in Brillinger (2002a) 1549.
4. Anscombe 296.
5. Wheeler in Brillinger (2002b) 193.
6. Descriptions of Tukey come from Anscombe 289, Bradford Murphy interview, and McCullagh 541.
7. Elizabeth Tukey and Tukey in Brillinger (2002a) 1561–2.
8. John Chambers, Bell Labs.
9. Ibid.
10. Tukey (1962) 5, 7.
11. Kotz and Johnson II 449.
12. Anscombe 294.
13. Bell Labs News (1985) (25) 18 and Brillinger (2002a) 1556.
14. Tukey in Brillinger (2002a) 1561.
15. Wallace interview.
16. Fienberg (2006) 24.
17. Wainer 285, Anscombe 290, and Wallace interview.
18. Box and Edgar Gilbert interviews, McCullagh 544 and 554, and Pratt interview, respectively.
19. Tukey (1967) in Jones (4) 589.
20. Tukey in Lyle V. Jones, (III) 108; (IV) xiv; (III) 188; and (III) 394, respectively.
21. Brillinger (2002a) 1561; L. Jones (1986) (IV) 771–2; Casella 312, respectively.
22. Casella 332 and McCullagh 547, respectively.
23. L. Jones (III) 277. “A natural . . . framework”: Casella 312.
24. Wallace, in interviews with the author.
25. Gnanadesikan.
26. L. Jones (IV) 589.
27. Brillinger interview.
28. Anscombe 300.
29. Wallace interview.
30. Brillinger e-mail.
31. Wallace interview.
14. Three Mile Island
1. In Lyle Jones (IV) 686 and Box and Tiao (1973) 1.
2. Bather 346–47 and Holmes interview, respectively.
3. Both Diaconis and Lindley recalled this incident in interviews.
4. Efron (1978) 232.
5. Lindley to Smith (1995) 313.
6. Apostalakis interview.
15. The Navy Searches
1. Quotations from John Craven are—unless noted otherwise—from interviews with the author.
2. Craven wrote The Silent War: The Cold War Battle Beneath the Sea at the navy’s behest in two weeks without notes in order to rebut the popular book Blind Man’s Bluff: The Untold Story of American Submarine Espionage (1998) by Sontag and Drew. In his own book, Craven said he attended Raiffa’s lectures; later he told me that he probably heard about Raiffa’s work from others at MIT.
3. Wagner (1988).
4. Ibid., 9.
5. Quotations from Henry R. (“Tony”) Richardson are from interviews with the author.
6. Capt. Frank A. Andrews e-mail.
7. Richardson interview.
8. Lewis 99–100, 133, 165, 168. Her Pulitzer Prize–winning book is generally regarded as the best on-site source.
9. Craven 173.
10. Lewis 206 and 208.
11. Wagner 10.
12. Craven 205–7.
13. Stone (1975) 54.
14. Craven 202–3.
15. Stone et al. (1999) ix.
16. Joseph H. Discenza interview.
17. Stone (1999) ix and (1983) 209.
18. Ibid., (1999) ix.
19. VAdm. John “Nick” Nicholson interview.
20. Ray Hilborn interview.
16. Eureka!
1. A. Philip Dawid interview.
2. In Donald Owen (1976) 421.
3. Cooke 20.
4. Jeffrey E. Harris interview.
5. Adrian Raftery interview.
6. Raftery (1986) 145–46.
7. Stuart Geman interview.
8. Shafer (1990) 440; and Diaconis in DeGroot (1986c) 334, respectively.
9. Lindley in Diaconis and Holmes (1996) 5 and in letter to the author.
10. AFM Smith (1984) 245, 255.
11. Alan Gelfand interview.
12. Christian Robert and George Casella.
13. Mayer in Householder 19.
14. W. Keith Hastings interview.
15. S. Gelfand interview.
16. Robert and Casella (2008).
17. Gelfand et al. (1990).
18. Gill 332.
19. Kuhn.
20. David Spiegelhalter interview.
21. Spiegelhalter, Abrams, and Myles.
22. Taylor and Gerrodette (1993).
23. Raftery interview.
24. Paul R. Wade interview.
25. Blackwell in DeGroot (1986a).
26. Diaconis and Holmes (1996) 5.
27. Sir John Russell and William Gladstone in the nineteenth century and Harold Wilson in the twentieth.
17. Rosetta Stones
Almost all the quotations in this chapter come from interviews with the author. Exceptions are noted here.
1. Unwin 190; Schneider; Ludlum 394. The phrase “We’re all Bayesians now” is sometimes attributed to John Maynard Keynes, but it may have first appeared in 1976 in John C. Henretta and Richard T. Campbell’s article, Status Attainment and Status Maintenance: A Study of Stratification in Old Age in American Sociological Review (41) 981–92. To complicate matters, Campbell was paraphrasing an earlier popular expression, “We’re all Keynesians now,” which has been attributed to Milton Friedman in 1966 and which was “popularized” by President Richard Nixon in 1971.
I am indebted to Stephen Senn, Michael Campbell, and Wikipedia for helping sort out the origins of the “Keynesians” quotation.
2. Dawid in Swinburne (2002) 84
3. Greenspan.
4. Ibid.
5. New York Times January 4, 2009.
6. Weaver 15.
glossary
algorithm a formula defining a sequence of steps in order to solve a problem
analysis a higher branch of mathematics
a priori see prior
axiom an assumption upon which a mathematical theory is based
ban a measure of probability expressed in logarithms to the base 10 so that multiplication can be replaced by addition
Bayes’ rule a mathematical device combining prior information with evidence from data (its formula appears on p. 31 with a simplified version on p. 257.)
Bayesian network a graphical model that compactly represents probabilities and their relationships. Each random variable is denoted by a node, and a line between two nodes indicates their interdependency.
centering points types of averages, e.g., the mean, median, and mode
change point the point when change occurs in time-ordered data
credibility a measure of the credence that actuaries place in a particular body of claims experience as they set insurance policy rates
cryptography writing and breaking ciphers, communications that third parties cannot understand
curse of high dimensionality the explosive growth of data sets as more variables are added
data bits of information that can be represented numerically
fiducial probability R. A. Fisher’s controversial attempt to apply probability to unknown parameters without using Bayes’ rule or priors
filter a process that makes data immune to the noise in a system and that extracts information from the data
frequency a branch of probability theory that measures the relative frequency of an event that can be repeated over and over again under much the same conditions
generating function a mathematical shortcut for making approximations
hierarchical Bayes a method that develops mathematical models by breaking complex processes into stages called hierarchies
hypothesis a proposition that is to be tested or modified with new evidence
induction drawing conclusions about natural laws or regularities from an observation or experiment; the opposite of deduction
infer deriving natural laws and regularities from a well-defined statement or observation
inverse probability the branch of probability theory that draws conclusions about antecedents or causes of obs
erved events, e.g., Bayes’ rule
likelihood principle an approach to using Bayes’ theorem without assuming any prior probabilities
likelihood ratio the comparison between the probabilities of an observation when a hypothesis is true and when it is untrue
Markov chain a process that assumes the probability of an event depends only on the immediately preceding events
MCMC a process that combines Markov chains and the Monte Carlo procedure
model a mathematical system used to understand another mathematical, physical, biological, or social system
Monte Carlo method a computer method to simulate probability distributions by taking random samples
multivariate containing many unknowns and variables
naïve Bayes a special, fast kind of Bayesian network
null hypothesis a plausible hypothesis that might explain a particular set of data; a null hypothesis can be compared with other alternatives
odds the ratio of the probabilities that an event will either occur or not occur
operations research or operational research a scientific approach to decision making
parameter in a mathematical expression, a quantity that is normally assumed to be constant; the value of the constant, however, can be changed as conditions are changed
posterior in Bayes’ theorem, the probability of a conclusion after evidence has been considered
prior the probability of a hypothesis before new data is observed
probability the mathematics of uncertainty; the numerical measure of uncertainty
rotors the geared wheels on Enigma machines
sampling the selection of a finite number of observations in order to learn about a much larger statistical population
sequential analysis the continuous analysis of data as they arrive while taking into account the effect of previous data
statistics a branch of applied mathematics that measures uncertainty and examines its consequences
stopping rule a sampling method in which data are evaluated as they are collected; the sampling stops when significant results are obtained
subjective probability Bayesian probability, a measure of personal belief in a particular hypothesis
transforms mathematical tools that change one kind of function into another that is easier to use
bibliography
Abbreviations
JASA
Journal of the American Statistical Association