Appendix

HAMILTON REFERENCES EXTERIOR TO The Federalist

Code Volume Abbreviation number Title number Pages

Cont.-1 101 The Continentalist No. I I 243-248 Cont.-2 102 The Continentalist No. II I 248-253 Pac.-1 111 Pacificus No. I IV 432-444 Pac.-2 112 Pacificus No. II IV 445-455 Pac.-3 113 Pacificus No. III IV 456-460

Lodge, H. C., editor (1904). The works of Alexander Hamilton (Federal Edition). G. P. Putnam's Sons, New York and London. I and IV.

MADISON REFERENCES EXTERIOR TO The Federalist

Abbreviation: Neutral Trade

Title: An Examination of the British Doctrine, Which Subjects to Capture A Neutral Trade, Not Open in Time of Peace

Editor: Hunt, VII

Code Code number Pages number

201 204-211 211 202 214-225 212 203 226-235 213 204 235-243 214 205 243-251 215 206 251-259 216 207 259-270 217 208 270-278 218 209 278-285 219 210 285-293 220

283

Pages

293-301 302-310 310-319 319-325 325-334 334-340 340-349 349-357 357-366 366-375

284 APPENDIX

MADISON REFERENCES EXTERIOR TO The Federalist (cont.)

Code Abbreviation number Title Editor Pages

N.A.-1 121 The North American No. I Brant 571-580 N.A.-2 12~ The North American No. II Brant 580-587 Helv-1 131 Helvidius Number I (Congress) 611-621 Helv-2 132 Helvidius Number II (Congress) 621-630 Helv-3 133 Helvidius Nuinber III (Congress) 630-640 Helv-4 134 Helvidius Number IV (Congress) 64~645

Helv-5 135 Helviditis Number V (Congress) 646-654 M-1 301 Population and Emigration Hunt, VI 43-66 l\Ii:-2 315 Consolidation Hunt, VI 67-69 M-3 315 Public Opinion Hunt, VI 70 M-4 302 Money Hunt, VI 71-80 M-5 316 Government Hunt, VI 80-82 M-6 313 Charters Hunt, YI 83-85 M-7 314 Parties Hunt, VI 86 M-8 311 British Government Hunt, VI 87-88 M-9 311 Universal Peace Hunt, VI 88-91 N-1 315 Government of the Hunt, VI 91-93

United States N-2 312 Spirit of Governments Hunt, VI 93-95 N-3 314 Republican Distribution Hunt, VI 96-99

of Citizens N-4 316 Fashion Hunt, VI 99-101 N-5 312 Property Hunt, VI 101-103 N-6 314 The Union. Who Are Its Hunt, VI 104-105

Real Friends? N-7 313 A Candid State of Parties Hunt, VI 106-119 N-8 316 Who ,Are the Best Keepers Hunt, VI 12~123

of the Peopie's Liberties? N-9 141 Observations on the Hunt, V 284-294

"Draught of a Constitution for Virginia"

311 is formed by pooling M-8 and M-9; 312, N-2 and N-5; 313, M-6 and N-7; 314, M-7, N...:.3, and N-6; 315, M-2, M-3, and N-1; 316, M-5, N-4, and N-8.

Brant, 1., editor (1946). Two neglected Madison letters. The William and Mary Quarterly, III, 569-587.

Published by order of Congress (1865). Letters and other writings of James Madison. J. B. Lippincott & Co., Philadelphia. I, 1769-1793.

Hunt, G., editor (1904). The writings of James Madison. G. P. Putnam's Sons, New York and London. V, 1787-1790.

Hunt, G., editor (1906). The writings of James Madison. G. P. Putnam's Sons, New York and London. VI, 179~1802.

Hunt, G., editor (1908). The writings of James Madison. G. P. Putnam's Sons, New York and London. V1I, 1803-1807.

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GOOD, 1. J. (1952). Rational decisions. Journal of the Royal Statistical Society, Series B, Vol. 14, 107-114.

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HAMILTON, JOHN C., editor (1864). The Federalist. J. B. Lippincott & Co., Philadelphia.

HANLEY, MILES L. (1937). Word index to James Joyce's Ulysses. University of Wisconsin Press, Madison.

HARRISON, P. N. (1921). The problem of the Pastoral Epistles. Oxford University Press, Oxford.

HERD AN, G. (1956). Language as choice and chance. P. N oordhoff Ltd., Groningen, Holland. --- (1966). The advanced theory of language as choice and chance. Springer,

Berlin. HODGES, J. L., JR. (1950). Discriminatory analysis. 1. Survey of discriminatory

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Index

Symbols are listed under the entry, "Symbols." For additional names of individuals see Acknowledgments at the close of each Preface.

Adair, Douglass 2, 6, 10, 16, 285 Adams, L. La Mar 277, 285 Adjusted 2 x 2 tables

for high-frequency words 218-220 for low-frequency words 221

Adjustment factor in penalty study 183, 189-190

Agarkar, G. G. 273, 274 Anderson, T. W. 57,285 And Quiet Flows the Don 272, 273 Anscombe, F. J. 75, 97, 98, 285 Antilogs, table of 69 Approximations

need for 92-93, 119-120, 124, 266-267

to posterior expectations 138-154 to posterior modes and maximum

likelihood estimates 108-111 Aristotle 276, 277 Atlantic, The 39,243 Atwood, Angela 279 Authorship of the disputed Federalist

papers historical introduction 2-6 summary of results 263-264

Authorship problems conclusions 265 making simplified studies 249-251

Bacon, Francis 270,271 Bailey, Richard W. 268,269,272,

277,278,279,285,286

Bailey, S. A. 10, 285 Bayes'theorem 47-54,64, 112-113

for continuous variables 64 for discrete hypotheses 53-54 example of application 52-55 two stages of use 58-59, 112

Bayes, Thomas 1,285 Bayesian inference 1-2,50-51

abstract structure in classification problems 111-117

remarks and conclusions 264, 266-267

see also main study; robust Bayesian analysis

Beaton, Albert E. 43-44 Beckman, Bengt 287 Benson, Egbert 4 Benson lists 3,4, 5, 14 Berkson, Joseph 48-49,285 Beta distribution 63

291

of 7J 65,103 mean is a relative mode 107 in robust Bayesian analysis 219 role of the extreme tails 137 of T 63, 65, 103, 128

Bible, King James version 39,243 word rates for 244-248

Bible, The 270, 276, 277 Binomial dispersion index 24

frequency distribution of 28 Binomial distribution 23-24

fitted and compared to incidence distributions 24-28

292 INDEX

Blyman, Mary 212 Bona ventura 274 Bourne,E. G. 5, 252, 285 Bracketing the prior distribution

63-64, 1i6-117, 124 ff., 266 see also prior distributions; under-

lying constants Brainerd, Barron 269; 270, 271, 285 Brant, Irving 6, 284, 285 Brentano, C1. 274 Brewer 243, 286 Brougham, IIenry 274 Burr, Aaron 4 by

frequency distribution of rate 168 in penalty study 185-189 table of contributions to log odds

78

"Caesar" letters 251-252 Calibrating set of papers 200, 229

choice for weight-rate analysis 201 results for

in three-category analysis 237-238

in weight-rate analysis 207-:208 size relative to screening set 201

Carlson, Roger 215 Characteristic curve of composition

259 Charles XII (King of Sweden) 277 Cherry, L. L. 269, 287 Child, Sir Josiah 274 Classification parameter 111, 181 Classification problems

abstract structure 111 ff. conclusions 265-266 single vs. simultaneous 114

Cochran, William G. 155,286 Collocation 270, 274, 280 Combining evidence from several words

54-55 Commas, rate of 273, 274, 280 Composite Madison 195 Computer 268, 269

role of 269 UNIX 269

Conditional analysis 116-117 Contagious distributions 31,96 Contaminated normal distributions

214 Contextual dangers 18, 68, 249-250,

265-266 inadequate protection in secondary

studies 201,216,226, 236-237 introd.uced by Neutral Trade essays

·20-22 asymmetry of distribution of 'fJ

130-131 treatment in main study 68,

195-199 Cooke, Jacob E. 2, 4, 5, 6, 9, 10, 86,

286 Coolidge, Julian L. 47-49, 286 " Corrector" 5 Correlation a,nd dependence

in the abstract strUcture 111-116 between rates for different words

35-37 ; matrix for 11 words 161

between rates in successive blocks of text 23-28

effect on log odds 84, 155-163 frequency distribution of 36 multinomial 35 in the weight-rate study 200-201

Cumulants of the negative binomial distribution 94

Cut-points for rates rules for determining 231 table 232-233

D* 272,273 Damerau, Fred J, 281, 286 Darnell, A. C. 274,275,288 Davis, Miles 36,67,69, 105, 185 Delta method 139, 151

applied to sample moments 98, 127 Discriminant function 9, 200

assessing the results of 210-214 frequency distribution of 8 in the weight-rate analysis 201

Discrimination problems, see classification problems

Disputed authorships (Chapter 10) And Quiet Flow8 the Don 272, 273 Aristotle 276, 277 Bible, The 270, 276, 277 Economic history 274,275 forensic disputes 278-280 Howland will 279,280 Kesari 273,274 military history of Charles XII

277,278 Nachtwachen, Die 274 Shakespeare-Bacon 268,270,271 translations 277, 278, 281

"Disputed" papers 3-6 results for

main study 74-80,87 pilot study 14 robust Bayesian analysis 228 in summary 263-264 three-category analysis 241-242 weight-rate analysis 210-214

Distributional assumptions abstract structure 111-116 for discriminant functions 212-214 importance of careful study 264,

266 independence 103-104, 200-201 for parameters 103 for word frequencies 99, 118

Dolezel, Lobomir 269,285,286 Don Cossacks 272

Early Madison 195 Economic history 274, 275 Editing by Hamilton or Madison 15,

90 Ellegard, Alvar 269, 277, 279, 281,

286 Empirical Bayes procedures 115 enough

corrections to log odds approxi­mation 144

counts of occurrences by individual paper 12-14

in the pilot study 11-14 table of contributions to log odds 79

Enumerations 257

INDEX 293

Erdelyi, A. 148, 153, 286 Expectations, approximate evaluation

of, 8ee posterior expectation; two-point formulas

Expected and observed log odds compared 173-176

Expected and observed penalties compared 185-190 defined 184

Exterior set of papers 11-13, 40, 283, 284

Farringdon, Jill 277, 278, 286 Farringdon, Michael 277,278,286 Federali8t, The 1 ff.

conclusions on authorship 263-264 edition used in present study 7 editions of

Cooke 2, 6, 86, 286 Gideon 4, 5, 14, 15, 286 Lodge 7,287 McLean 4, 83, 286 Modern Library 7, 286 Sesquicentennial 7, 286 Rossiter 6, 289 Wright 6, 289

history of the authorship dispute 2-6, 14-15

late Hamilton papers 83 8ee also disputed papers; editing by

Hamilton or Madison; joint papers; papers of known authorship

Felice 77, 252 Fielding, Henry 277,278 Final odds (of authorship) 50, 54-59,

69 ff., 100, 112-114, 118-119, 219-224

8ee log odds believability 88-91 effect of outrageous events on

90-91 justification within the model

88-90 in the robust Bayesian analysis

219-229 tables of, see log odds

294 INDEX

Fisher, R. A. 1,97,286 Fix, Evelyn 286 Ford, Paul Leicester 5, 251, 286 Forensic disputes 268, 278-280 Fowles, John 270 Francis, Ivor S. 36, 126, 140, 165,

215, 235 Francis, W. Nelson 281, 287 Freeman, Murray F. 157,287 Frequency distributions

empirical (tables and figures) of adjectives 8 of category of use of of 255 of X2 statistics in tests of

binomiality 28 of correlations between word rates

36 of estimates of 11 131 of estimates of (J' and T 62 of incidence, for each of 51 words

25-27 of a measure of discriminating

ability 42 of nouns 8 of numbers of Hamilton papers

with a low rate 218 of occurrences, for each of 51

words 29-30; for each of 10 words 32-33

of one- and two-letter words 8

of values of a discriminant function 8

of word length 258,260-261 of word rates: also 167; an

167; both 171; by 17,168; commonly 18; from 17 ; innovation 18; of 168; on 169; the 8; there 169; this 170; though 172; to 17,170; upon 19, 171; war 19

theoretical (tables) fitted binomial frequencies for

incidence of each of 51 words 25-27

fitted negative binomial frequencies for occurrences of each of 10 words 32-33

fitted Poisson frequencies for occurrences of each of 10 words 32-33

Poisson with mean 2,31 Poisson and negative binomial

compared 34 two Poisson's compared 153

Friedman, E. A. 39, 288 Fries, C. C. 39, 287 Function words 17,39,280

list 38

Gallaher, Miriam 256 Gamma distribution 65, 95, 96

of 6 65,103 mean is a relative mode 107

Gill, Steinar 287 Gokhale, M. K. 273, 287 Good, I. J. 191, 287 Gore, A. P. 273, 287 Granger, Gideon 5 Green, Hetty 279 Gustavsson, Sven 287

Hamilton, Alexander 1 if. word rates for 244-248 see also authorship of the disputed

Federalist papers Hamilton, John Church 5, 287 Handlin, Joanna F. 253 Hanley Concordance 243, 287 Harris, Emily 279 Harrison, P. N. 276, 287 Hearst, Patricia 279 Herdan, G. 269,287 High-frequency words

in concordances 269 in the main study

contributions to log odds 78 in the robust Bayesian analysis

definition and list 217 method of obtaining log odds

217-220 distribution of 2 x 2 tables 218

see also words Historical information

role in formal analysis 113-114

Hodges, J. L., Jr. 286, 287 Hoel, P. G. 24, 287 Hoffman,E.T.A. 274 Homogeneity problems 275-277 Hoodes, Robert A. 43 Howland, Sylvia 279 Howland will 268, 279, 280 Hunt, G. 283-284

Importance of a word in the main study 55-56,58,

158-159; table 158 in the weight-rate analysis

202-204; table 204 Independence

in the abstract structure 111, 115 of historical evidence 113 in the main study 99 of observations 274, 275 of variables 280 in the weight-rate analysis 200, 201 see also correlation and dependence

Index of performance in screening study

41-42 word index 42-43

Inefficient estimates 111 Information

Fisher 97 Shannon 191

Ingalls, Theodore S. 44 Initial odds (of authorship} 50,54-59,

. 112-114 Integrals, approximate evaluation of,

see posterior expectation

"Jackknife" technique 126-127 James, Henry 270 James, William 39 Jay,John 2,3,4,5,243

comparison with Hamilton and Madison 248

text used 243 word rates for 244-248

Jefferson, Thomas 3,5,9 Jeffreys, Harold 2, 213, 287

INDEX 295

"Joint" papers 3-6 further analysis of Paper No. 20

252-253 results for

main study 74 pilot study 14 robust Bayesian analysis 228

. in summary 263-264 three-category analysis 241-242 weight-rate analysis 210-214

Joshi, S. B. 273,287 Joyce, James 243-248 Junius 271,277,281

}(enny,llnthony 269,276,277,287 }(ent, Chancellor James 4-5 }(ent list 4-5, 14 Kesari 273, 274 }(jetsaa, Geir 272, 273, 287 }(leyle, Robert 133, 243, 259 }(lingemann, E. A. 274 }(nown papers, see papers of known

authorship }(ryukov, Fyodor 272,273 }(ucera, Henry 281,287

Laplace integral expansion 148, 153 applied to posterior expectations

multivariate 150-151 univariate 148

asymptotic development 153-154 transformation of variables 149,

152 Late Hamilton papers 83 Late Madison 195 Length of paper, see paper length Likelihood ratio 54-57,120-124

behavior of negative binomial 97, 122-124 Poisson 122

for correlated normals 155, 160 discussion of desirable shapes

120-121 estimates and confidence limits for,

in the weight-rate analysis 212-214

296 INDEX

Likelihood ratio (continued) monotone 122-124 see also log odds; odds factors

Linear discriminant function, see discriminant function

Littauer Statistical Center, Harvard University 43

Lodge, Henry Cabot 5, 71, 283, 287 Log odds 55

see also final odds in the main study

adjustments to 84-88; in penalty study 189-190

comparison of Poisson and negative binomial 75, 81

conditional and unconditional 118-119

contributions of marker and high-frequency words 81-82

effects of correlations 155-163 illustrated for 15 pairs of words

157-159; for 11 words treated jointly 160-161

mean and variance of adjustment 155-156, 160

effects of systematic variations in Madison's writings 195-199; table 196

effects of varying the prior distributions, see prior distributions, effects ofvarying

evaluation of 119-120 expected log odds

under the negative binomial model 178-180; table 164

under a normal approximation 155-156; table 158

under the Poisson model 177 ; table 164

in total, compared to observed log odds 173; paper-by­paper 174-175

by word group 176 tables of

by individual words 78-80 in total for the disputed and

joint papers 74; adjusted 88

in total for the late Hamilton papers 83

in total for the papers of known authorship 70-73

by word groups 76 in the robust Bayesian analysis

for high-frequency words 217-220

for low-frequency words 220-224

tables for disputed and joint papers 229; for papers of known authorship 225-228

in the three-category analysis interpretation 238-239 role as weights 229 rules for computing 233 table 232-233

in the weight-rate analysis 213-214; table 213

Low-frequency words in the robust Bayesian analysis

definition and list 217 method for obtaining log odds

220-224 weakness of using rates 201, 220 see also marker words; words

Madison, James 1 ff. word rates for 244-248 see also authorship of the disputed

Federalist papers Main study 46-199

abstract structure 111-117 methods illustrated for Poisson

model 51-64 results on authorship

for disputed and joint papers 74-75, 87-88

for papers of known authorship 69-73, 75

summarized 263-264 theoretical basis 92-199 two stages of analysis 58-59

Marker words 10-11 log odds for 77-82

Marlowe, Christopher 270

Mathematical model 22 Matrix inversion

use of a simple approximation 162-163

Maximum likelihood estimation iterative determination 105, 108

choice of initial values 108-111 negative binomial 97

McCulloch, J. R. 274 McMahon, L. E. 269,287 Medvedev, Roy A. 272, 273, 287 Meier, Paul 279, 287 Mendenhall, T. C.259, 270,271,287,

288 Method-of-moments estimates

in a binomial problem 129-130 in choice of Pl and P2 125-130 as initial estimates for iteration

108....;111 of negative binomial parameters

97-98 tables for 22 words 101; for

30 words 110 Method parameter p, see model

parameter; prediction method Mill, James 274 Mill, John Stuart 274 Miller, G. A. 7,39,288 Miller-Newman-Friedman list 28,

37-39, 243-248, 250, 288 sources 243 word rates for 244-248

Minimum penalty estimation 188 Mitchell, Ann 212 Mitchell, Broadus 6, 288 Mixture assumption in study of

systematic variation 195, 198-199

Modal approximation 60, 100, 119 in the abstract structure 116-117 accuracy. 85-86 methods for studying accuracy

138-154 illustrated for 5 words 143-'-146

which mode 1 104-105, 106-108 Modal estimates 67, 104-107

choice of initial estimate 108-111 iterative determination 105

table of 66, 110 for upon 136

INDEX 297

which'mode1 104-107, 139-140, 149

Model parameter p 99, 163, 181 Model II analysis of variance 52, 115 Molina, E. C. 31, 288 Monotone likelihood ratio, see

likelihood ratio Mood; A. M. 213, 288 Morris, R. 269, 287 Morton, A. Q. 268, 269, 270, 276, 278,

281, 288 Mosteller, F. 6-10, 23, 42, 43, 288

Nabokov, Vladimir 272 N achtwachen; Die 274 Negative binomial distribution 34-35,

51, 65, 93-98, 99 cumulants 94 formula 34, 93 likelihood function 97 likelihood ratio and its behavior

97, 122-124 limiting behavior 94-95 mixture representation 95, 96 parameters

choice of 96-97 estimation 97-98, 100-101 for pairs of distribution 102-103 prior distributions 65, 103; see

also prior distributions table of estimates for final words

66; of method-of-moments estimates for 22 words 101

penalty study of adequacy 185-190 possible strange behavior illustrated

for upon 135-138 relation to Poisson 93-95 sample moments 98

Newman, E. B. 39,288 Newman, Morris 163,288 Newton-Raphson iteration 105 Nonparametric methods 274,275 Non-Poissonness 35,94,96-97

combined 102 differential 101-102

298 INDEX

N on-Poissonness (continued) estimates for 22 words 100-101 transformations of 101-102,

140-141 Nuisance parameters

formal analysis 114-117

Oakman, Robert L. 269, 288 O'Brien, D. P. 274,275,288 Odds 9,53-54

see log odds; final odds; odds factor Odds factor 100,112-114,117-120 Odoroff, Charles L. 126, 140, 165, 203 of

frequency by category of use 255-256

on corrections to approximate log odds

144-145 correlation 84, 157-159 frequency distribution of rate 169 in penalty study 185-189 table of contributions to log odds

78 Outrageous events 90-91

P-values for assessing discrimination 211

Paper, defined and identified 17, 19-21;283-284

Paper length adjustments in study of regression

effects 178, 180 adjustments to log odds in robust

Bayesian analysis 221, 224 denoted by w 52, 93 as a discriminator 259 for screening and calibrating sets

209 table of 70-74; means 178

Papers of disputed and joint authorship, see disputed papers; joint papers

Papers of known authorship exterior to The Federalist 283-284 from The Federalist 3-6, 70-73

results for main study 69-73 pilot study 12-13 robust Bayesian analysis

235-239 three-category analysis 225-227 weight-rate analysis 205-208

Parameters classification 111 of data distributions 57, 60-67 distribution of estimates 62, 107 model 99 of prior distributions 52, 63; see

also underlying constants treated as random variables 58,

60 see also prior distributions; posterior

distributions; negative binomial distribution, parameters

Particles and connectives 276 Parts of speech 276 Paul,Jean 274 Pearson, Egon S. 48-49,288 Peirce, Benjamin 279 Peirce, Charles Sanders 279 Penalties

expected defined 184 relation to Shannon information

191 table of bench-mark values 185 tables for the Federalist

application 186-188 observed

choice of penalty function 191 comparison with expected

185-190 defined 184, 191 effect of adjustment factor

189-190 effect of initial odds 188-189 likelihood interpretation 192-195 minimizing, as an estimation

procedure 188 relation to log odds 192 standardized deviate 185 tables for the Federalist

application 186-190

Penalty function basis of choice 190-192 in Federalist application 183-190 minimization property 184, 191 table of bench-mark values 185 see also penalties

Penalty study 180-195 adequacy of Poisson and negative

binomial models 185-190 specification and labeling of methods

182-183 test sequence 181-182 see penalty function; penalties

Petersen, David L. 277,288 Phrases 45 Poetry versus prose 268, 270, 271 Poisson distribution 28, 31-34, 51,

95-96, 97, 99 fitted and compared to observed

and negative binomial distributions 32-34

likelihood ratio 122 penalty study of adequacy 185-190 used to describe methods for main

study 51-64 Pollatschek, Moshe A. 277,289 Portnoy, Stephen L. 277,288 Position of word in sentence 270,

274 Posterior distributions

in the abstract structure 116-117 illustrated for also 64 mode of 60, 67, 105-107

tables 66, 85 see also modal estimates

of parameters 58-59, 103-105 relative density, 107 standard deviations of 85

Posterior expectations approximate evaluation 138-154

components of error 143-144 multivariate 150-152 using means and variances 139 using modes and derivatives

139 see Laplace integral expansion

asymptotic theory 152-154 as an integral 60, 139

INDEX 299

Prediction method 181-183 comparisons, for the Federalist

application 185-190 expected and observed penalties

184 Prior distributions 48-49

see also underlying constants choice of 61, 100-102, 124-138 effects of varying 63,67,75,84-85,

132-138 tables 70-74, 134

empirical base 61-62, 266 of negative binomial parameters (1',

T, g, n 65, 103, 124-138 of parameters 58-59, 61-67, 103,

114-116 of Poisson parameters (1', T 61-63 in robust Bayesian analysis

choice of 220, 223 high-frequency words 219 low-frequency words 222

Probability of authorship, see final odds; log

odds; initial odds interpretation 47-50 see also odds; prior distributions;

posterior distributions Probability predictions

defined 181 evaluating methods of 180-195

Proportionate pairs 269, 280 "Publius" 2

Radday, Yehuda T. 277,288,289 Raiffa, H. 214, 289 Range 202 Rao, C. R. 57,289 Rao, P. S. R. S. 241 Rates, see word rates Regression effects

in the main study 163-180 expected and observed rates

compared 165-166 by single words 240-241 in the three-category analysis

239-241 in the weight-rate analysis 208-209

300 INDEX

Relative density 107 Relative mode 104-107, 139-140, 149 Rencher, Alvin C. 277,285 Robbins, Herbert 115, 289 Roberts, Paul 9, 289 Robinson, Hetty (Hetty Green) 279 Robust Bayesian analysis 215-228

methods 215-224 results

for disputed and joint papers 228 for papers of known authorship

225-227 Robustness 215 Rossiter, Clinton 6; 289 Rourke, R. E. K. 23,288 Runyon, Damon 75,289, Rush, Richard 5 Rush list 5

Savage, L. J. 51 Schelling, Fr. 274 Schlaifer, Robert 214, 289 Scott, Sir Walter 269,270 Screening set of papers 200, 229

choice of in robust Bayesian analysis

216-217 in three-category analysis ~29 in weight-rate analysis 201

results for in robust Bayesian analysis

225-226 in three-category analysis

235-236 in weight-rate analysis 205-206

Screening study 11,39-42, 250-251 list of words obtained 38

Selecting words, methods of for possible qse in study 37-43 in simplified studies 249-251 for use in final inference

main study 54-55,67-69, 195-198

robust Bayesian analysis 216-217

three-category anlJ,lysis 229-234 weight-rate analysis 201, 203

Selection effects 51-52,67-68,200,275 illustrated, for also 64

Sentencelength 6-7,273,280 average 7 standard deviation 7

Shakespeare, William 270,271 Shakespeare-Bacon controversy 268,

270, 271 Shannon, C. 191 Sholokhov, MikhlJ,il 272,273 Shore, Haim 277,288,289 Sidney, Sir Philip 271 Simultaneous classification ~O, 114,

182 Smirp.ov, N. V. 214, 289 Solzhenitsyn,AIeksandr 272 Spacing of frequent words 281 Square~root transformation 157 Stages of analysis 58-{!0

block diagram 59 St!tlin, Joseph 272 Standardized deviate

for observed penalty 185 Stewart, Ralph A., Jr. 43 Stigler, Stephen M. 275,289 Strength of a word, see importance of

., a word Strong Concordance 243, 289 Stylistics 269 boo~s on 269

Stylometrics 2~9, 270 Suffix convention 150 Sukhatme, P. V. 214,289 Symbols: a partial list of those used in

several sections with a common meaning (subscripts are omitted here)

d 98, 100 fnb 93 fp 95 m 61 nb 93, 99 P 99 s 61 t 62 w 52, 93 a 103 fl 63, 65, 103

Symbols (continued) P* 107 Y 103 (in Sections 4.2, 4.6 only) o 93-94 'YJ 102 o 111 K 93-94 It 52,93-94, 111 g 102 u 61, 102 T 61, 102 ¢ 99 A 106, 140 ~ 59,94

Synonyms 256 Systematic variation in Madison's

writings 68, 195-199

t-statistics for assessing discrimination 210-211

log odds from t 212-214 Tails of distributions

contrast between prior and data distributions 138

and likelihood ratio behavior 120-121

and robustness 215 Temple, Sir William 77, 252 Test sequence, see penalty study, test

sequence Thomas, G. B., Jr. 23, 288 Three-category analysis 229-242

method 229-234 results

for disputed and joint papers 241-242

for papers of known authorship 235-239

study of regression effects 239-241 to

corrections to approximate log odds 144

frequency distribution of rate 170 in penalty study 185-189 rates in different groups of writings

198 table of contribution to log odds 78

Tilak, B. G. 273, 274 Tolstoy, Leo 272 Torrens, R. 274

INDEX 301

Transition frequencies 274, 280 Translations 277, 278, 281 Tukey, John W. 42,126,157,288,289 Two-point formulas for expected log

odds 179-180 2000-word set of papers 173, 216

identified 216 log odds for 225-226 mean paper lengths 178

Type-token ratio 273

Ulysses 243 word rates for 244-248

Underlying constants choice of Pi and P2 124-130; of Pa

130-131; of P4 and Ps 131-132

defined 52, 63, 115 effect of varying, see prior

distributions, effect of varying formally specified 65, 103 in relation to alternative choice of

modes 107 sets used

complete table 102 final choices 65 initial choices 63 to study effects of varying prior

distributions 132 upon

changes in counts 86 comparison of observed and

expected log odds 176 corrections to approximate log odds

144-145 correlation 84, 157-159 counts of occurrences by individual

paper 12-14 detailed study of likelihood and of

log odds 135-138 discovery 11 empirical and theoretical

distributions of occurrences 32, 33

302 INDEX

upon (continued) frequency distribution of rate 19,

171 justification of magnitude of odds

89 performance in secondary studies,

paper-by-paper 204-210, 225-228, 232,235~239, 242

table of contributions to log odds in the main study 76

Validating set of papers 216 log odds for 226-228

Validation ofthe main study 69,75,83

penalty study 181-190 regression study 163-176

of the robust Bayesian 226-228 of the three-category analysis

236-239 of the weight-rate analysis

207-208 Variables for discrimination (Chapter

10) collocation 270, 274, 280 commas, rate of 273, 274, 280 function words 280 particles and connectives 276 parts of speech 276 position of word in sentence 270,

274 proportionate pairs 269, 280 sentence length 273,280 spacing of frequent words 281 transition frequencies 274, 280 type-token ratio 273 word frequencies 274,275 word length 270, 271, 273, 280

Variables for discrimination (The Federalist) 16, 45

see words; word rates . miscellaneous unsuccessful choices

256-257,259 phrases 45 sentence length 6-7 word length 259-262 words classified by use 252-256

Wallace, D. L. 43, 288 Waves A, B, C of papers 11-13,

39-42 Weight-rate analysis 200-214

method 200-203 results

for disputed and joint papers 210-214

for papers of known authorship, 205-208

study of regression effects 208-209 Weights for word rates 202,204 "Well-liked" words 68,204 Wetzel, F. G. 274 while-whilst

changes in counts 86 corrections to approximate log odds

144, 146 counts of occurrences by individual

papers 12-14 initial discovery 10 in the pilot st-ddy 10-14 table of contributions to log odds

79-80 Wickmann, Dieter 274,277,289 Wiitanen, Wayne 43 Williams, C. B. 6, 259, 269, 270, 271,

273,289 Williams, Frederick 6-10 Willson, C. Harvey 43 Word counts

distribution of, see frequency distributions

effect of errors and changes on log odds 86-87

by hand 44 by machine 43-44 paper-by-paper, for four words

12-14 suggested simplified method 250

Word frequencies 274,275 counting difficulties 269 distributional assumptions

formal 99 heuristic 96

high-frequencies 269, 270, 276 Word groups

for the main study 68-69, 77

Word groups (continued) log odds by 76-77, 83 regression effect by 176

for the robust Bayesian analysis 217

for the three-category analysis 234 results by 235-242

for the weight-rate analysis 203-204

results by 205-210 Word length

comparisons of Bacon, Shakespeare, and Sidney 271

comparisons of Hamilton's and Madison's 261-262

as a discriminating variable 258-262, 270, 271, 280

distributions of 258, 260, 261, 271 273

Word rates 17 correlation between pairs of words

35-37 matrix for 11 words 161 dependence in successive blocks of

text 23-28 distributions of 28-35 mathematical models for describing

22 ff. systematic deviations between The

Federalist and Neutral Trade 68, 194-198

tables of distributions in Hamilton, Madison

and disputed papers for 11 words 167-172; see also

INDEX 303

frequency distributions for Madison over time 21 for 165 words in 6 sources of

writing 244-248 observed and expected, for 11

words 166 variation with time 19-22

Words 16 contextual 18, 39, 51, 68, 204 function 17, 38-39 marker 10-11 meanings and uses 253-256 pools 37--43

role in main study 51-52 used in final inference

main study 66 robust Bayesian analysis 217 three-category analysis 232-233 weight-rate analysis 203-204

used in study 38,43 well-liked 68, 204 see also selection of words; word

length; word rates; by; enough; of; on; to; upon; while-whilst

Wright, Benjamin Fletcher 6, 289 Wundt, Wilhelm 7, 290

Yeager, Marie 133,243,259 Youtz, Cleo 43, 126 Yule, G. Ddny 6, 269, 290

Zabell, Sandy 279, 287

Symbols are listed under the entry, "Symbols." For additional names of individuals see Acknowledgments at the close of each Preface.

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