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L. Billard 325bounce around, so that an apparent rate of 64 (say) may really be 64 ± 2, i.e.,the interval [62, 66]. There are numerous examples.Detailed descriptions and examples can be found in Bock and Diday (2000)and Billard and Diday (2006). A recent review of current methodologies isavailable in Noirhomme-Fraiture and Brito (2011), with a non-technical introductionin Billard (2011). The original concept of symbolic data was introducedin Diday (1987). Note that symbolic data are not the same as fuzzy data;however, while they are generally different from the coarsening and groupingconcepts of, e.g., Heitjan and Rubin (1991), there are some similarities.The major issue then is how do we analyse these intervals (or, histograms,...)? Taking classical surrogates, such as the sample mean of aggregatedvalues for each category and variable, results in a loss of information.For example, the intervals [10, 20] and [14, 16] both have the same midpoint;yet they are clearly differently valued observations. Therefore, it is importantthat analytical methods be developed to analyse symbolic data directly so asto capture these differences. There are other underlying issues that pertainsuch as the need to develop associated logical dependency rules to maintainthe integrity of the overall data structure; we will not consider this aspectherein however.29.3 IllustrationsExample 29.1 Table 29.1 displays (in two parts) a data set of histogramvalued observations, extracted from Falduti and Taibaly (2004), obtained byaggregating by airline approximately 50,000 classical observations for flightsarriving at and departing from a major airport. For illustrative simplicity,we take three random variables Y 1 = flight time, Y 2 = arrival-delay-time,and Y 3 = departure-delay-time for 10 airlines only. Thus, for airline u =1,...,10 and variable j =1, 2, 3, we denote the histogram valued observationby Y uj = {[a ujk ,b ujk ),p ujk : k =1,...,s uj } where the histogram sub-interval[a ujk ,b ujk )hasrelativefrequencyp ujk with ∑ k p ujk = 1. The number ofsubintervals s uj can vary across observations (u) and across variables (j).Figure 29.1 shows the tree that results when clustering the data by aWard’s method agglomerative hierarchy algorithm applied to these histogramdata when the Euclidean extended Ichino–Yaguchi distance measure is used;see Ichino and Yaguchi (1994) and Kim and Billard (2011, 2013), for details.Since there are too many classical observations to be able to build an equivalenttree on the original observations themselves, we resort to using classicalsurrogates. In particular, we calculate the sample means for each variableand airline. The resulting Ward’s method agglomerative tree using Euclideandistances between the means is shown in Figure 29.2.
326 The present’s futureTABLE 29.1Airline data.Y 1 [0, 70) [70, 110) [110, 150) [150, 190) [190, 230) [230, 270)1 .00017 .10568 .33511 .20430 .12823 .0452672 .13464 .10799 .01823 .37728 .35063 .011223 .70026 .22415 .07264 .00229 .00065 .000004 .26064 .21519 .34916 .06427 .02798 .018485 .17867 .41499 .40634 .00000 .00000 .000006 .28907 .41882 .28452 .00683 .00076 .000007 .00000 .00000 .00000 .00000 .03811 .307938 .39219 .31956 .19201 .09442 .00182 .000009 .00000 .61672 .36585 .00348 .00174 .0000010 .76391 .20936 .01719 .00645 .00263 .00048Y 2 [−40, −20) [−20, 0) [0, 20) [20, 40) [40, 60) [60, 80)1 .09260 .38520 .28589 .09725 .04854 .030462 .09537 .45863 .30014 .07433 .03226 .016833 .12958 .41361 .21008 .09097 .04450 .027164 .06054 .44362 .33475 .08648 .03510 .018655 .08934 .44957 .29683 .07493 .01729 .037466 .07967 .36646 .28376 .10698 .06070 .037947 .14024 .30030 .29573 .18293 .03659 .010678 .03949 .40899 .33727 .12483 .04585 .022249 .07840 .44599 .21603 .10627 .04530 .0331010 .10551 .55693 .22989 .06493 .02363 .01074Y 3 [−15, 5) [5, 25) [25, 45) [45, 65) [65, 85) [85, 105)1 .67762 .16988 .05714 .03219 .01893 .014632 .84993 .07293 .03086 .01964 .01683 .004213 .65249 .14071 .06872 .04025 .02749 .016694 .77650 .14516 .04036 .01611 .01051 .005265 .63112 .24784 .04323 .02017 .02882 .002886 .70030 .12064 .06297 .04628 .02049 .012907 .73323 .16463 .04726 .01677 .01220 .003058 .78711 .12165 .05311 .01816 .00772 .006359 .71080 .12369 .05749 .03310 .01916 .0052310 .83600 .10862 .03032 .01408 .00573 .00286It is immediately apparent that the trees differ, even though both havethe same “determinant” — agglomerative, Ward’s method, and Euclideandistances. However, one tree is based on the means only while the other isbased on the histograms; i.e., the histogram tree of Figure 29.1, in addition tothe information in the means, also uses information in the internal variances ofthe observed values. Although the details are omitted, it is easy to show that,e.g., airlines (1, 2, 4) have similar means and similar variances overall; however,by omitting the information contained in the variances (as in Figure 29.2),
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ContentsPrefacexviiContributorsI Th
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viii15 We live in exciting times 15
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x24.6 Open areas for research . . .
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xii36 Buried treasures 405Michael A
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xiv45.3 Multi-phase inference . . .
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PrefaceStatistics is the science of
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PrefacexixPart V comprises seven ar
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xxiiNancy FlournoyUniversity of Mis
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Part IThe history of COPSS
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4 A brief history of COPSSOnchiota
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6 A brief history of COPSSThe items
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8 A brief history of COPSSTABLE 1.1
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10 A brief history of COPSSwomen of
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12 A brief history of COPSSTABLE 1.
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16 A brief history of COPSS1.4.3 Ge
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20 A brief history of COPSSFor more
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2Reminiscences of the Columbia Univ
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I. Olkin 25Bechhofer, Allan Birnbau
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I. Olkin 27Milton Sobel was the tea
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3AcareerinstatisticsHerman Chernoff
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H. Chernoff 31given three-day basic
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H. Chernoff 33Savage tried to defen
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H. Chernoff 35In working on an arti
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H. Chernoff 37measure the loss as t
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H. Chernoff 39ReferencesAlbert, A.E
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4“. . . how wonderful the field o
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D.R. Brillinger 43He went on to be
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D.R. Brillinger 45Tukey wrote many
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D.R. Brillinger 4718. Personal comm
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50 Unorthodox journey to statistics
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6Statistics before and after my COP
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P.J. Bickel 616.3.1 Imperial Colleg
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P.J. Bickel 63make. This was first
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P.J. Bickel 65We eventually develop
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P.J. Bickel 67school interest, biol
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P.J. Bickel 69ReferencesBean, D., B
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P.J. Bickel 71Meinshausen, N., Bick
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74 Accidental biostatistics profess
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84 Passion for statisticsme is its
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86 Passion for statisticsTheir Biom
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88 Passion for statisticsthe first
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90 Passion for statisticsIn my expe
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92 Passion for statistics8.5 Job an
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94 Passion for statisticsperiod. An
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96 Passion for statisticsNeyman, J.
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98 Reflections on a statistical car
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100 Reflections on a statistical ca
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110 Science mixes it up with statis
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11Lessons from a twisted career pat
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J.S. Rosenthal 119My math professor
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J.S. Rosenthal 121contrary, it null
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J.S. Rosenthal 123of statistical re
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J.S. Rosenthal 125be open to whatev
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J.S. Rosenthal 12711.4 Final though
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130 Promoting equityand fellowship
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132 Promoting equityevaluate such e
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134 Promoting equityfor equity. But
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136 Promoting equityAssistant Secre
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Part IIIPerspectives on the fieldan
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142 Statistics in service to the na
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154 Where are the majors? ArtBachel
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156 Where are the majors?References
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158 Exciting timesCritically, Efron
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160 Exciting timesIn general I find
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162 Exciting timesI entered the Uni
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164 Exciting times15.3.3 Joining th
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166 Exciting timesvariability of a
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168 Exciting timesHabemma, J.D.F.,
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16The bright future of applied stat
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R.A. Irizarry 173FIGURE 16.1Illustr
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R.A. Irizarry 17516.4 The bright fu
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17The road travelled: From statisti
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N. Chatterjee 179the Kaplan-Meyer e
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N. Chatterjee 18117.4 Genome-wide a
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N. Chatterjee 183by any means. I ju
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N. Chatterjee 185right information
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N. Chatterjee 187The risk of cancer
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190 Journey into genetics and genom
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19Reflections on women in statistic
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M.E. Thompson 205Pearson in England
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M.E. Thompson 207TABLE 19.1The 14 C
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M.E. Thompson 209time series, the s
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M.E. Thompson 211the founding Chair
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M.E. Thompson 21319.7 The current s
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M.E. Thompson 215Yarmie, A. (2003).
Page 239 and 240:
218 “The whole women thing”seem
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220 “The whole women thing”of t
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222 “The whole women thing”on a
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224 “The whole women thing”20.5
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226 “The whole women thing”Ifin
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228 “The whole women thing”Lond
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230 Reflections on diversityas a st
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232 Reflections on diversityall of
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234 Reflections on diversityforce m
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22Why does statistics have two theo
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D.A.S. Fraser 23922.2 65 years and
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D.A.S. Fraser 241function is taken
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D.A.S. Fraser 24322.4 Inference for
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D.A.S. Fraser 245that record the ef
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D.A.S. Fraser 247variable that give
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D.A.S. Fraser 249simple scalar case
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D.A.S. Fraser 251DiCiccio, T.J. and
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23Conditioning is the issueJames O.
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J.O. Berger 255Pedagogical example:
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J.O. Berger 257The SRP does not say
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J.O. Berger 25923.5 Conditional fre
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J.O. Berger 261conditional error pr
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J.O. Berger 263others). If x is the
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J.O. Berger 265How does a frequenti
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24Statistical inference from aDemps
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A.P. Dempster 269tion is simply une
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A.P. Dempster 271As the world of st
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A.P. Dempster 273when the X i are a
Page 296 and 297: A.P. Dempster 27524.5 Nonparametric
Page 298 and 299: A.P. Dempster 277can easily happen
Page 300 and 301: A.P. Dempster 279ReferencesBorel,
Page 302 and 303: 25Nonparametric BayesDavid B. Dunso
Page 304 and 305: D.B. Dunson 283troduced, providing
Page 306 and 307: D.B. Dunson 285els in spatial stati
Page 308 and 309: D.B. Dunson 287methods as also prov
Page 310 and 311: D.B. Dunson 289ing background, and
Page 312: D.B. Dunson 291Murray, J.S., Dunson
Page 315 and 316: 294 Choosing default methodsimagine
Page 317 and 318: 296 Choosing default methods(a) mat
Page 319 and 320: 298 Choosing default methodspartial
Page 321 and 322: 300 Choosing default methodsdirecti
Page 324 and 325: 27Serial correlation and Durbin-Wat
Page 326 and 327: T.W. Anderson 305The characteristic
Page 328 and 329: T.W. Anderson 307Consider the seria
Page 330 and 331: 28Anon-asymptoticwalkinprobabilitya
Page 332 and 333: P. Massart 311(at least for discret
Page 334 and 335: P. Massart 31328.2.2 Non-asymptopia
Page 336 and 337: P. Massart 315where P = sµ. In oth
Page 338 and 339: P. Massart 317Hence by Talagrand’
Page 340 and 341: P. Massart 319ReferencesAkaike, H.
Page 342: P. Massart 321Talagrand, M. (1995).
Page 345: 324 The present’s futuredata. In
Page 349 and 350: 328 The present’s future124356981
Page 351 and 352: 330 The present’s futuremethod, t
Page 353 and 354: 332 The present’s futureFIGURE 29
Page 355 and 356: 334 The present’s futureIchino, M
Page 357 and 358: 336 Lessons in biostatistics30.2 It
Page 359 and 360: 338 Lessons in biostatisticsprognos
Page 361 and 362: 340 Lessons in biostatisticstime fo
Page 363 and 364: 342 Lessons in biostatisticsmeaning
Page 365 and 366: 344 Lessons in biostatistics75% to
Page 367 and 368: 346 Lessons in biostatisticshistolo
Page 370 and 371: 31AvignetteofdiscoveryNancy Flourno
Page 372 and 373: N. Flournoy 351FIGURE 31.1Incidence
Page 374 and 375: N. Flournoy 353FIGURE 31.3Mean resp
Page 376 and 377: N. Flournoy 355FIGURE 31.4Kaplan-Me
Page 378 and 379: N. Flournoy 357As the study proceed
Page 380 and 381: 32Statistics and public health rese
Page 382 and 383: R.L. Prentice 36132.2 Public health
Page 384 and 385: R.L. Prentice 363from urinary excre
Page 386 and 387: R.L. Prentice 36532.5 Clinical tria
Page 388: R.L. Prentice 367Kaplan, E.L. and M
Page 391 and 392: 370 Statistics in a new erative eff
Page 393 and 394: 372 Statistics in a new eraular com
Page 395 and 396: 374 Statistics in a new erajoint de
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376 Statistics in a new eraof the n
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378 Statistics in a new eraLai, T.L
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34Meta-analyses: Heterogeneity can
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N.M. Laird 383into the sum of a “
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N.M. Laird 385are “approximately
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N.M. Laird 387included in the major
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N.M. Laird 389Yusuf, S., Peto, R.,
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392 Good health: Statistical challe
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406 Buried treasuresmeasurement tec
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408 Buried treasuresIn a most rewar
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410 Buried treasureslems different
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37Survey sampling: Past controversi
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R.J. Little 41537.2 Probability or
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R.J. Little 417for the “design-ba
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R.J. Little 419estimate of variance
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R.J. Little 421Example 2 continued
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R.J. Little 42337.3.4 The design-mo
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R.J. Little 42537.5 ConclusionsI am
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R.J. Little 427Isaki, C.T. and Full
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38Environmental informatics: Uncert
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N. Cressie 431and conquer” strate
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N. Cressie 433In the last 20 years,
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N. Cressie 435Once the satellite ha
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N. Cressie 437FIGURE 38.1Locations
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N. Cressie 439regional and seasonal
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N. Cressie 441ciated with the spati
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N. Cressie 443is the set of all pix
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N. Cressie 445challenge is to devel
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N. Cressie 447Gourdji, S.M., Muelle
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N. Cressie 449Wikle, C.K., Milliff,
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452 Statistical geneticsTABLE 39.1T
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454 Statistical geneticsStewart, 19
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456 Statistical geneticslocidata
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458 Statistical geneticssufficientl
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460 Statistical geneticsBrown, M.D.
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462 Statistical geneticsLange, K. a
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464 Statistical geneticsThompson, E
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466 Targeted learningods for nonpar
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468 Targeted learningdenote the obs
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470 Targeted learningSuch an estima
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472 Targeted learningliterature pro
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474 Targeted learninglihood estimat
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476 Targeted learning40.6 Some spec
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478 Targeted learningmemory challen
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480 Targeted learningvan der Laan,
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482 Ah-ha momentwe have just seen.
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484 Ah-ha momentthe data is unchang
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486 Ah-ha momentis well defined and
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488 Ah-ha momentit was something of
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490 Ah-ha momentdefines a Euclidean
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492 Ah-ha momentparticipate in the
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494 Ah-ha momentLee, Y., Wahba, G.,
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42In praise of sparsity and convexi
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R.J. Tibshirani 499TABLE 42.1Asampl
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R.J. Tibshirani 501CancerEpithelial
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R.J. Tibshirani 503that the error v
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R.J. Tibshirani 505Tibshirani, R.J.
Page 529 and 530:
508 Features of Big Dataproblems en
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510 Features of Big Datalearning st
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512 Features of Big Data1210(a)p =
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514 Features of Big Data25002000150
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516 Features of Big DataAs an illus
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518 Features of Big Datafor some gi
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520 Features of Big Data43.7.3 Prop
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522 Features of Big DataBühlmann,
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44Rise of the machinesLarry A. Wass
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L.A. Wasserman 527if an idea requir
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L.A. Wasserman 529●●●● ●
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L.A. Wasserman 531●●●●●
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L.A. Wasserman 533FIGURE 44.4Simula
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L.A. Wasserman 53544.7 Education an
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45Atrioofinferenceproblemsthatcould
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X.-L. Meng 539it is directly rooted
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X.-L. Meng 541exactly, but this doe
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X.-L. Meng 543That is, when we do n
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X.-L. Meng 545(a) For what classes
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X.-L. Meng 547subsequent analysts c
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X.-L. Meng 549can prove only that (
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X.-L. Meng 551In general, “What t
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X.-L. Meng 553vironmental progress
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X.-L. Meng 555which will be compare
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X.-L. Meng 557(a) Given partial kno
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X.-L. Meng 559AcknowledgementsThe m
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X.-L. Meng 561Knuth, D. (1997). The
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Part VAdvice for the nextgeneration
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566 Inspiration, aspiration, ambiti
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568 Inspiration, aspiration, ambiti
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47Personal reflections on the COPSS
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R.J. Carroll 573them is, by definit
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R.J. Carroll 575(Carroll, 2003). In
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R.J. Carroll 57747.8 After the Pres
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R.J. Carroll 579Carroll, R.J., Spie
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582 Publishing without perishingthe
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584 Publishing without perishingbeg
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586 Publishing without perishingme,
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588 Publishing without perishingalr
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590 Publishing without perishingpor
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49Converting rejections into positi
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D.B. Rubin 595This pair of submissi
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D.B. Rubin 597There are several les
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D.B. Rubin 599very sound article, w
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D.B. Rubin 60149.8 ConclusionIhaveb
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D.B. Rubin 603Rubin, D.B. (1972). A
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606 Importance of mentorstwice as t
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608 Importance of mentorsexperiment
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610 Importance of mentorsposition a
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612 Importance of mentors50.7 The t
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51Never ask for or give advice, mak
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T. Speed 617overly generous. Perhap
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T. Speed 619and for finding enjoyme
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622 Thirteen rules3. Waste a lot of
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